23238.A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line?
0.80 mm
0.70 mm
0.50 mm
0.75 mm
23239.If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be
[E V–2 T–1]
[E V–1 T–2]
[E V–2 T–2]
[E–2 V–1 T–3]
23240.Which of the following units denotes the dimensions ML2/Q2, where Q denotes the electric charge?
Weber (Wb)
Wb/m2
Henry (H)
H/m2
23241.If n denotes a positive integer, h the Planck’s constant, q the charge and B the magnetic field, then the quantity $\dfrac{nh}{2\pi qB}$ has the dimension of
area
length
speed
acceleration
23242.The dimension of magnetic field in M, L, T and C (Coulomb) is given as
MLT–1C–1
MT2C–2
MT–1C–1
MT–2C–1
23243.The period of oscillation of a simple pendulum is $T = 2\pi\sqrt{\dfrac{L}{g}}$. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The accuracy in the determination of g is
2%
3%
1%
5%
23244.A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading : 0 mm
Circular scale reading : 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions of the circular scale.
The diameter of wire from the above data is
Main scale reading : 0 mm
Circular scale reading : 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions of the circular scale.
The diameter of wire from the above data is
0.005 cm
0.52 cm
0.052 cm
0.026 cm
23245.A wire of length l = 6 ± 0.06 cm and radius r = 0.5 ± 0.005 cm and mass m = 0.3 ± 0.003 gm. Maximum percentage error in density is
4
2
1
6.8
23246.In the expression for Boyle’s law, the product ‘PV’ has dimensions of
force
impulse
energy
momentum
23247.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 : $P = \dfrac{a^3b^2}{cd}$. % error in P is
14%
10%
7%
4%
23248.Let [ε0] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:
[ε0] = [M–1L–3T4A2]
[ε0] = [M–1L2T–1A–2]
[ε0] = [M–1L2T–1A]
[ε0] = [M–1L–3T2A]
23250.The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is
0.9%
2.4%
3.1%
4.2%
23251.The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10–3 are
4, 4, 2
5, 1, 2
5, 1, 5
5, 5, 2