A screw gauge has least count of 0.01 mm and there
are 50 divisions in its circular scale. The pitch of the
screw gauge is :

A screw gauge has least count of 0.01 mm and there
are 50 divisions in its circular scale. The pitch of the
screw gauge is :

4 Mark(s)

(a) 0.01 mm

(b) 0.25 mm

(c) 0.5 mm

(d) 1.0 mm

The dimensions of RC is :

The dimensions of RC is :

4 Mark(s)

(a) square of time

(b) square of inverse time

(c) time

(d) inverse time.

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be :

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be :

4 Mark(s)

(a)

(b)

(c)

(d)

The ratio of the dimensions of Planck’s constant and that of moment of inertia is the dimensions of :

The ratio of the dimensions of Planck’s constant and that of moment of inertia is the dimensions of :

4 Mark(s)

(a) time

(b) frequency

(c) angular momentum

(d) velocity

Which pair do not have equal dimensions ?

Which pair do not have equal dimensions ?

4 Mark(s)

(a) Energy and torque

(b) Force and impulse

(c) Angular momentum and Planck’s constant

(d) Elastic modulus and pressure

Which two of the following five physical parameters have the same dimensions ?
1. energy density
2. refractive index
3. dielectric constant
4. Young’s modulus 5. magnetic field :

Which two of the following five physical parameters have the same dimensions ?
1. energy density
2. refractive index
3. dielectric constant
4. Young’s modulus 5. magnetic field :

4 Mark(s)

(a) 1 and 4

(b) 1 and 5

(c) 2 and 4

(d) 3 and 5

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are :

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are :

4 Mark(s)

(a)

(b)

(c)

(d)

The pair of quantities having same dimensions is :

The pair of quantities having same dimensions is :

4 Mark(s)

(a) Impulse and Surface Tension

(b) Angular momentum and Work

(c) Work and Torque

(d) Young’s modulus and Energy

A particle covers half of its total distance with speed \(v_{2}\) and the rest half distance with speed \(v_{2}\). Its average speed during the complete journey is :

A particle covers half of its total distance with speed \(v_{2}\) and the rest half distance with speed \(v_{2}\). Its average speed during the complete journey is :

4 Mark(s)

(a)

(b)

(c)

(d)

The dimensions of \({(\mu_{0} \varepsilon_{0})}^{-1 / 2}\) are :

The dimensions of \({(\mu_{0} \varepsilon_{0})}^{-1 / 2}\) are :

4 Mark(s)

(a)

(b)

(c)

(d)

The dimensions of universal gravitational constant are :

The dimensions of universal gravitational constant are :

4 Mark(s)

(a)

(b)

(c)

(d)

Of the following quantities, which one has dimensions different from the remaining three ?

Of the following quantities, which one has dimensions different from the remaining three ?

4 Mark(s)

(a) Energy per unit volume

(b) Force per unit area

(c) Product of voltage and charge per unit volume

(d) Angular momentum

The dimension of \({1 \over 2 }{\varepsilon^{0}E^{2}}\), where \({\varepsilon_{0}}\) is permittivity of free space and E is electric field, is :

The dimension of \({1 \over 2 }{\varepsilon^{0}E^{2}}\), where \({\varepsilon_{0}}\) is permittivity of free space and E is electric field, is :

4 Mark(s)

(a)

(b)

(c)

(d)

. If x = at + \(bt^{2}\) , where x is the distance travelled by the body in kilometers while t is the time in seconds, then the units of b is :

. If x = at + \(bt^{2}\) , where x is the distance travelled by the body in kilometers while t is the time in seconds, then the units of b is :

4 Mark(s)

(a) km/s

(b) km s

(c)

(d)

The unit of thermal conductivity is :

The unit of thermal conductivity is :

2 Mark(s)

(a)

(b)

(c)

(d)

The dimensions of Planck’s constant equals to that of:

The dimensions of Planck’s constant equals to that of:

4 Mark(s)

(a) energy

(b) momentum

(c) angular momentum

(d) power

Taking into account of the significant figures, what is the value of 9.99 m – 0.0099 m? :

Taking into account of the significant figures, what is the value of 9.99 m – 0.0099 m? :

4 Mark(s)

(a) 9.9801 m

(b) 9.98 m

(c) 9.980 m

(d) 9.9 m

Which of the following is a dimensional constant? :

Which of the following is a dimensional constant? :

4 Mark(s)

(a) Relative density

(b) Gravitational constant

(c) Refractive index

(d) Poisson’s ratio

If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be :

If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be :

4 Mark(s)

(a) 8%

(b) 2%

(c) 4%

(d) 6%

A certain body weighs 22.42 g and has a measured volume of 4.7cc. The possible error in the measurement of mass and volume are 0.01 g and 0.1 cc. Then maximum error in the density will be :

A certain body weighs 22.42 g and has a measured volume of 4.7cc. The possible error in the measurement of mass and volume are 0.01 g and 0.1 cc. Then maximum error in the density will be :

1 Mark(s)

(a) 22%

(b) 2%

(c) 0.2%

(d) 0.02%.

Dimensions of stress are :

Dimensions of stress are :

4 Mark(s)

(a)

(b)

(c)

(d)

If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as [hxryrz] where h, r and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by :

If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as [hxryrz] where h, r and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by :

4 Mark(s)

(a) –1, –1, –1

(b)1, 1, 1

(c)1, –1, –1

(d)–1, –1, 1

A physical quantity of the dimensions of length that can be formed out of c, G and \({e^{2} \over 4 \pi \varepsilon_{0}}\)is [c is velocity of light, G is the universal constant of gravitation and e is charge] :

A physical quantity of the dimensions of length that can be formed out of c, G and \({e^{2} \over 4 \pi \varepsilon_{0}}\)is [c is velocity of light, G is the universal constant of gravitation and e is charge] :

4 Mark(s)

(a)

(b)

(c)

(d)

According to Newton, the viscous force acting between liquid layers of area A and velocity gradient \(\Delta v/ \Delta Z\) is given by \(F=- \eta A{\Delta v \over \Delta Z}\), where \(\eta\) is constant
called coefficient of viscosity. The dimensional formula of \(\eta\) is :

According to Newton, the viscous force acting between liquid layers of area A and velocity gradient \(\Delta v/ \Delta Z\) is given by \(F=- \eta A{\Delta v \over \Delta Z}\), where \(\eta\) is constant
called coefficient of viscosity. The dimensional formula of \(\eta\) is :

4 Mark(s)

(a)

(b)

(c)

(d)

The dimensions of impulse are equal to that of :

The dimensions of impulse are equal to that of :

4 Mark(s)

(a)

(b)

(c)

(d)

The dimensional formula of permeability of free space \(\mu^{0}\) is :

The dimensional formula of permeability of free space \(\mu^{0}\) is :

4 Mark(s)

(a)

(b)

(c)

(d)

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular
scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of –0.004 cm, the correct diameter of the ball is :

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular
scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of –0.004 cm, the correct diameter of the ball is :

3 Mark(s)

(a) 0.521 cm

(b) 0.525 cm

(c) 0.053 cm

(d) 0.529 cm

Percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring
mass and speed will be :

Percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring
mass and speed will be :

4 Mark(s)

(a) 8%

(b) 2%

(c) 12%

(d) 10%.

If C and R denote capacitance and resistance, the dimensional formula of CR is :

If C and R denote capacitance and resistance, the dimensional formula of CR is :

4 Mark(s)

(a)

(b)

(c)

(d)

The dimensional formula of torque is :

The dimensional formula of torque is :

4 Mark(s)

(a)

(b)

(c)

(d)

In an experiment, four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows

\(p= {a^{3} \ b^{2} \over cd}. \). % error in P is :

In an experiment, four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows

\(p= {a^{3} \ b^{2} \over cd}. \). % error in P is :

4 Mark(s)

(a) 7%

(b) 4%

(c) 14%

(d) 10%

A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is :

A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is :

4 Mark(s)

(a)

(b)

(c)

(d)

The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation \(f=am^{x}k^{y}\) where a is a dimensionless constant. The values of x and y are

The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation \(f=am^{x}k^{y}\) where a is a dimensionless constant. The values of x and y are

4 Mark(s)

(a)

(b)

(c)

(d)

The density of a material in CGS system of units is \(4 \ g \ cm^{-3}\).In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of
density of material will be :

The density of a material in CGS system of units is \(4 \ g \ cm^{-3}\).In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of
density of material will be :

4 Mark(s)

(a) 0.04

(b) 0.4

(c) 40

(d) 400

P represents radiation pressure, c represents speed of light and S represents radiation energy striking per unit area per sec. The non zero integers x, y, z such that \(p^{x}s^{y}c^{z}\)

is dimensionless are :

P represents radiation pressure, c represents speed of light and S represents radiation energy striking per unit area per sec. The non zero integers x, y, z such that \(p^{x}s^{y}c^{z}\)

is dimensionless are :

4 Mark(s)

(a)

(b)

(c)

(d)

The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and lengths are 3% and 2% respectively, the maximum error in the measurement of density would be :

The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and lengths are 3% and 2% respectively, the maximum error in the measurement of density would be :

4 Mark(s)

(a) 12%

(b) 14%

(c) 7%

(d) 9%.

If the dimensions of a physical quantity are given by \({M^{a}L^{b}T^{c}}\) , then the physical quantity will be :

If the dimensions of a physical quantity are given by \({M^{a}L^{b}T^{c}}\) , then the physical quantity will be :

4 Mark(s)

(a) velocity if a = 1, b = 0, c = – 1

(b) acceleration if a = 1, b = 1, c = – 2

(c) force if a = 0, b = – 1, c = – 2

(d) pressure if a = 1, b = –1, c = –2

Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length ? :

Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length ? :

4 Mark(s)

(a) x = 1, y = 1, z = 1

(b) x = –1, y = 1, z = 1

(c) x = 1, y = –1, z = 1

(d) x = 1, y = 1, z = –1

In an experiment, the percentage of error occurred
in the measurement of physical quantities A, B, C
and D are 1%, 2%, 3% and 4% respectively. Then the
maximum percentage of error in the measurement :

In an experiment, the percentage of error occurred
in the measurement of physical quantities A, B, C
and D are 1%, 2%, 3% and 4% respectively. Then the
maximum percentage of error in the measurement :

4 Mark(s)

(a)10%

(b)(3/13)%

(c)16%

(d)–10%

If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are :

If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are :

4 Mark(s)

(a)) [FVT–1]

(b)[FVT–2]

(c)[FV–1T–1]

(d)[FV–1T]

Dimensional formula of self inductance is :

Dimensional formula of self inductance is :

4 Mark(s)

(a)

(b)

(c)

(d)

The dimensional formula of angular momentum is :

The dimensional formula of angular momentum is :

4 Mark(s)

(a)

(b)

(c)

(d)

Which of the following has the dimensions of pressure?

Which of the following has the dimensions of pressure?

4 Mark(s)

(a)

(b)

(c)

(d)

An equation is given here \(\left( P + \frac {a}{V^2}\right)=b \ {\Theta \over V}\)where P = Pressure, V = Volume and \(\theta\) = Absolute temperature. If a and b are constants, the dimensions
of a will be :

An equation is given here \(\left( P + \frac {a}{V^2}\right)=b \ {\Theta \over V}\)where P = Pressure, V = Volume and \(\theta\) = Absolute temperature. If a and b are constants, the dimensions
of a will be :

4 Mark(s)

(a)

(b)

(c)

(d)

The unit of permittivity of free space, \(ε_{0}\) , is :

The unit of permittivity of free space, \(ε_{0}\) , is :

2 Mark(s)

(a)

(b)

(c)

(d)

The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (n – 1) divisions of main scale. The least count of the vernier callipers is

The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (n – 1) divisions of main scale. The least count of the vernier callipers is

4 Mark(s)

(a)

(b)

(c)

(d)

The time dependence of a physical quantity p is given by \(P=P_{0} \ exp (-at_{2})\), where a is a constant and t is the time. The constant a :

The time dependence of a physical quantity p is given by \(P=P_{0} \ exp (-at_{2})\), where a is a constant and t is the time. The constant a :

4 Mark(s)

(a)

(b)

(c)

(d)

The dimensional formula of magnetic flux is :

The dimensional formula of magnetic flux is :

4 Mark(s)

(a)

(b)

(c)

(d)

The velocity v of a particle at time t is given by \(V=at+{b \over t+c}\), where a, b and c are constants. The dimensions of a, b and c are :

The velocity v of a particle at time t is given by \(V=at+{b \over t+c}\), where a, b and c are constants. The dimensions of a, b and c are :

4 Mark(s)

(a)

(b)

(c)

(d)

Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is P. The viscosity of oil is given by \(\eta = {p(r^{2}-x^{2}) \over4vl}\)

where v is the velocity of oil at a distance x from the axis of the tube. The dimensions of \(\eta\)are :

Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is P. The viscosity of oil is given by \(\eta = {p(r^{2}-x^{2}) \over4vl}\)

where v is the velocity of oil at a distance x from the axis of the tube. The dimensions of \(\eta\)are :

4 Mark(s)

(a)

(b)

(c)

(d)

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