(a, d)

Suppose at an instant 't' velocity of cart be v. Due to the sand falling on the cart, it experiences a retarding force, which is equal to µv. It means net accelerating force on the cart is equal to (F – µv). But at this instant, mass of the loaded cart is equal to (m 0 + µt).

Therefore, acceleration at time t will be equal to . It means, option is wrong.

If in above equation t is substituted as zero, then initial acceleration of the cart is, a 0 =

But at initial moment, speed of flat cart is equal to zero. Hence, the initial acceleration becomes (F/m 0 ). It means, option is correct.

If we consider a system of flat cart and falling sand particles, then sand particles exert a retarding force on the cart which is equal to µv and the cart exerts an accelerating force on sand particles which is also equal to µv. It means the only external force or the only resultant force acting on the system is equal to F.

It means the momentum of the system at any instant t will be equal to impulse of the force F. Hence, option is correct.

The collision of the sand particles with the cart is perfectly inelastic because just after falling on the cart, sand particles start to move horizontally rightward with the cart while just before coming onto the cart, these sand particles have zero horizontal velocity. It means there is a loss of energy during the collision. Hence, kinetic energy of loaded cart at an instant will be less than the work done by the force F up to that instant. Hence, option is wrong.