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 division
Given that 1 mm on the main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is

• 0.052 cm

• 0.026 cm

• 0.005

• 0.005

A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R.Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

• g

• 2/3g

• g/3

• g/3

Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly. (Surface tension of soap solution = 0.03 Nm^-1)

• 4π mJ 

• 0.2π mJ

• 2π mJ

• 2π mJ

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc 

• remains unchanged

• continuously decreases

• continuously increases 

• continuously increases 

Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is

• -4Gm/r

• -6Gm/r

• -9Gm/r

• -9Gm/r

6.

Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d(d < < l) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate.As a result the charges approach each other with a velocity v. Then as a function of distance x between them

• v ∝ x^-1

• v ∝ x^1/2

• v ∝ x

• v ∝ x

An object moving with a speed of 6.25m/s, is decelerated at a rate given by dv/dt =- 2.5√v, where v is the instantaneous speed. The time taken by the object, to come to rest, would be

• 2 s

• 4 s

• 8 s

• 8 s

A pulley of radius 2m is rotated about its axis by a force F = (20t - 5t²) Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg-m², the number of rotations made by the pulley before its direction of motion if reversed is

• more than 3 but less than 6

• more than 6 but less than 9

• more than 9

• more than 9

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is

The transverse displacement y(x,t) of a wave on a string is given by

This represents a

• wave moving in +x direction with speed 

• wave moving in -x direction with speed 

• standing wave frequency 

• standing wave frequency