Units and Measurements

Given a charge q, current I and permeability of vacuum 0. Which of the following quantity has the dimension of momentum ?

1. qI/ 0
2. q2 0 I
3. q 0/I
4. q 0 I

The pair of physical quantities not having the same dimensions is :

1. Angular momentum and Planck's constant
2. Torque and energy
3. Surface tension and impulse
4. Pressure and Young's modulus

The expression given below shows the variation of velocity (v) with time (t), v = At2 + BtC + t. The dimension of ABC is :

1. [ M0L1T-2]
2. [ M0L2T-3]
3. [ M0L2T-2]
4. [ M0L1T-3]

For an experimental expression y= 32.3 112527.4, where all the digits are significant. Then to report the value of y we should write

1. y=1326.186
2. y=1326.2
3. y=1326.19
4. y=1330

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation

1. E2=pc2+m2c4
2. E2=pc2+m2c2
3. E2=p2c2+m2c4
4. E2=p2c2+m2c2

The position of a particle moving on x-axis is given by x(t)=A t+B 2t+Ct2+D, where t is time. The dimension of ABCD is

1. L
2. L3 T-2
3. L2 T-2
4. L2

The electric flux is = + where and are linear and surface charge density, respectively. ( ) represents

1. displacement
2. charge
3. electric field
4. area

The energy of a system is given as E(t)= 3e- t, where t is the time and =0.3 s-1. The errors in the measurement of and t are 1.2\% and 1.6\%, respectively. At t=5 s, maximum percentage error in the energy is :

1. 6\%
2. 11.6\%
3. 4\%
4. 8.4\%

If B is magnetic field and 0 is permeability of free space, then the dimensions of (B/ 0) is

1. MT-2A-1
2. L-1A
3. ML2T-2A-1
4. LT-2A-1

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below.

1. Both Statement I and Statement II are false
2. Statement I is true but Statement II is false
3. Both Statement I and Statement II are true
4. Statement I is false but Statement II is true

Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge respectively.

1. [F]= [ C M-1L-2T2 ]
2. [F]= [ C2M-2L2T2 ]
3. [F]= [ C2M-1L-2T2 ]
4. [F]= [ C M-2L-2T-2 ]

The maximum percentage error in the measurement of density of a wire is [Given, mass of wire =(0.60 0.003) g radius of wire =(0.50 0.01) cm length of wire =(10.00 0.05) cm]

1. 7
2. 8
3. 5
4. 4

The dimensional formula of latent heat is :

1. [ M0LT-2]
2. [ MLT-2]
3. [ M0L2T-2]
4. [ ML2T-2]

One main scale division of a vernier caliper is equal to m units. If nth division of main scale coincides with (n + 1)th division of vernier scale, the least count of the vernier caliper is :

1. 1(n + 1)
2. m(n + 1)
3. n(n + 1)
4. mn(n + 1)

The de-Broglie wavelength associated with a particle of mass m and energy E is h/ 2mE. The dimensional formula for Planck's constant is :

1. [ M2 L2 T-2 ]
2. [ ML-1 T-2 ]
3. [ ML2 T-1 ]
4. [ MLT-2 ]

In an expression a 10b :

1. a is order of magnitude for b 5
2. b is order of magnitude for a 5
3. b is order of magnitude for a 5
4. b is order of magnitude for 5 < a 10

Young's modulus is determined by the equation given by Y = 49000 Ml dynecm2 where M is the mass and l is the extension of wire used in the experiment. Now error in Young modulus (Y) is estimated by taking data from M–l plot in graph paper. The smallest scale divisions are 5 g and 0.02 cm along load axis and extension axis respectively. If the value of M and l are 500 g and 2 cm respectively then percentage error of Y is :

1. 2%
2. 0.02%
3. 0.5%
4. 0.2%

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm. The main scale reading is 2 cm and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g, the density of the sphere is:

1. 2.2 g/cm3
2. 2.0 g/cm3
3. 1.7 g/cm3
4. 2.5 g/cm3

If o is the permittivity of free space and E is the electric field, then oE2 has the dimensions :

1. [ ML-1 T-2]
2. [ ML2 T-2]
3. [ M0L-2TA]
4. [ M-1 L-3 T4 A2]

There are 100 divisions on the circular scale of a screw gauge of pitch 1 mm. With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is :

1. 4.65 mm
2. 4.60 mm
3. 4.55 mm
4. 3.35 mm

Least count of a vernier caliper is 120 N cm. The value of one division on the main scale is 1 mm. Then the number of divisions of main scale that coincide with N divisions of vernier scale is :

1. ( 2N - 12N )
2. ( 2N - 120N )
3. (2N - 1)
4. ( 2N - 12 )

To find the spring constant (k) of a spring experimentally, a student commits 2\% positive error in the measurement of time and 1\% negative error in measurement of mass. The percentage error in determining value of k is :

1. 5\%
2. 3\%
3. 1\%
4. 4\%

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the wire is x50 mm. The value of x is :

1. 42
2. 71
3. 21
4. 142

Given below are two statements: In the light of the above statements, choose the most appropriate answer from the options given below.

1. Statement (I) is incorrect but statement (II) is correct
2. Both statement (I) and statement (II) are incorrect
3. Both statement (I) and statement (II) are correct
4. Statement (I) is correct but statement (II) is incorrect

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 4th division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm then how many main scale divisions are there in 1 cm ?

1. 5
2. 40
3. 10
4. 20

If G be the gravitational constant and u be the energy density then which of the following quantity have the dimensions as that of the uG :

1. Gravitational potential
2. pressure gradient per unit mass
3. Energy per unit mass
4. Force per unit mass

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s, 4.632 s, 4.6 s and 4.64 s. The arithmetic mean of these readings in correct significant figure is :

1. 5 s
2. 4.6 s
3. 4.62 s
4. 4.623 s

What is the dimensional formula of ab-1 in the equation (P + aV2 )(V - b) = RT, where letters have their usual meaning.

1. [M6 L7 T4]
2. [ M-1 L5 T3]
3. [ M0 L3 T-2]
4. [ M L2 T-2]

A vernier callipers has 20 divisions on the vernier scale, which coincides with 19th division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to mm.

1. 5
2. 2
3. 1
4. 0.5

The equation of stationary wave is : y=2a ( 2 ) ( 2 x ). Which of the following is NOT correct :

1. The dimensions of nt is [L]
2. The dimensions of n is [ LT-1]
3. The dimensions of x is [L]
4. The dimensions of n/ is [T]