One end of a string of length l is connected to a particle of mass ‘m’ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed ‘v’, the net force on the particle (directed towards centre) will be (T represents the tension in the string)

• T

• 
• 
• 

The x and y coordinates of the particle at any time are x = 5t – 2t² and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s is

• 0

• 5 m/s²

• -4 m/s²

• -4 m/s²

Suppose the charge of a proton and an electron differ slightly. One of them is –e, the other is (e + Δe). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given mass of hydrogen
mh = 1.67 × 10^–27 kg]

• 10^–20 C

• 10^–23 C

• 10^–37 C

• 10^–37 C

The diagrams below show regions of equipotentials

A positive charge is moved from A to B in each diagram.

• Maximum work is required to move q in figure (c).

• In all the four cases the work done is the same.

• Minimum work is required to move q in figure (a).

• Minimum work is required to move q in figure (a).

The physical quantity of the dimensions of length that can be formed out of c, G and e/4πε0 is [c is the velocity of light, G is the universal constant of gravitation and e is charge]

Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s]

• 350 Hz

• 311 Hz

• 411 Hz

• 411 Hz

The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then

• d =1/2 km

• d = 1 km

• d =3/2 km

• d =3/2 km

Which of the following statements is correct?
(a) Centre of the mass of a body always coincides with the centre of gravity of the body.
(b) Centre of the mass of a body is the point at which the total gravitational torque on the body is zero
(c) A couple on a body produce both translational and rotational motion in a body.
(d) Mechanical advantage greater than one means that small effort can be used to lift a large load.

• (b) and (d)

• (a) and (b)

• (b) and (c)

• (b) and (c)

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current ‘I’ along the same direction is shown in Fig. Magnitude of force per unit length on the middle wire ‘B’ is given by

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:

• Keep floating at the same distance between them

• Move towards each other

• Move away from each other

• Move away from each other