A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v= α√x . The displacement of the particle varies with time as

• t³

• t²

• t

• t^1/2

B.

t²

A bomb of mass 16 kg at rest explodes into two pieces of masses of 4 kg and 12 kg. The velocity of the 12 kg mass is 4 ms⁻¹ . The kinetic energy of the other mass is

• 144 J

• 96 J

• 288 J

• 192 J

A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of 45° with the initial vertical direction is

• 
• 
• 
• 

A.

A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. the work done by the force of gravity during the time the particle goes up is

• 0.5 J

• -0.5 J

• −1.25 J

• 1.25 J

C.

−1.25 J

The potential energy of a 1 kg particle free move along the x-axis is given by

The total mechanical energy of the particle 2 J. Then, the maximum speed (in m/s) is

• 2

• 
• 
• 

B.