Units and Measurements

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]

Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.

1. T2 = 4 2 rGM2
2. T2 = 4 2 r3
3. T2 = 4 2 r3GM
4. T2 = 4 2 r2GM

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

1. 511
2. 1011
3. 5011
4. 12

The dimensional formula of angular impulse is :

1. [ ML2T-2]
2. [ ML-2T-1]
3. [ ML2T-1]
4. [ MLT-1]

The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as r=(0.35 0.05) cm R=(100 10) ohm l=(15 0.2) cm The percentage error in resistivity of the material of the wire is :

1. 37.3\%
2. 25.6\%
3. 35.6\%
4. 39.9\%

Match List - I with List - II. Choose the correct answer from the options given below :

1. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
2. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
3. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
4. (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

If the percentage errors in measuring the length and the diameter of a wire are 0.1\% each. The percentage error in measuring its resistance will be:

1. 0.144%
2. 0.2%
3. 0.1%
4. 0.3%

A force is represented by F=ax2+bt 12 where x= distance and t= time. The dimensions of b2/a are:

1. [ ML2 T-3 ]
2. [ ML3 T-3 ]
3. [ MLT-2 ]
4. [ ML-1T-1 ]

Consider two physical quantities A and B related to each other as E= B-x2At where E, x and t have dimensions of energy, length and time respectively. The dimension of AB is

1. L-2M1T0
2. L2M-1T1
3. L0M-1T1
4. L-2M-1T1

The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is:

1. 6
2. 5
3. 4
4. 8

Match List I with List II. Choose the correct answer from the options given below :

1. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
2. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
3. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
4. (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is 0.5 mm, the Vernier constant of traveling microscope is

1. 0.01 mm
2. 0.01 cm
3. 0.1 mm
4. 0.1 cm

If mass is written as m=kcPG-1/2h1/2 then the value of P will be : (Constants have their usual meaning with k a dimensionless constant)

1. 1/3
2. -1/3
3. 1/2
4. 2