Units and Measurements

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