A particle of mass 500 gm is moving in a straight line with velocity v = b x^5/2. The work done by the net force during its displacement from x = 0 to x = 4 m is : (Take b = 0.25 m^$$-$$3/2 s^$$-$$1).

A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is :

(Given : initial temperature of the bullet = 127$$^\circ$$C, Melting point of the bullet = 327$$^\circ$$C, Latent heat of fusion of lead = 2.5 $$\times$$ 10⁴ J kg^$$-$$1, Specific heat capacity of lead = 125 J/kg K)

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass?

(Assume the collision to be head-on elastic collision)

In the arrangement shown in figure a₁, a₂, a₃ and a₄ are the accelerations of masses m₁, m₂, m₃ and m₄ respectively. Which of the following relation is true for this arrangement?