Question ID - 100611 | SaraNextGen Top Answer
A flat cart of mass 
starts moving to the right due to a constant horizontal force 
at 
. Sand spills on the flat cart from a stationary hopper. The velocity of loading is constant and is equal 
kg/s
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|
a) |
Initial acceleration is equal to |
|
b) |
Acceleration at time |
|
c) |
Kinetic energy of loaded cart at an instant is equal to work done by force |
|
d) |
Momentum of loaded cart at an instant is equal to impulse of force |
is
up to that instant
up to that instant(a,d)
Let at an instant ‘
’, velocity of cart be 
. Due to the sand falling on the cart, it experiences a retarding force, which is equal to 
It means net accelerating force on the cart is equal to 
. But at this instant, mass of the loaded cart is equal to 
Therefore, acceleration at time 
will be equal to 
It means option (b) is incorrect.
If in the above equation, 
is substituted as zero, then initial acceleration of the cart is
But an initial moment, speed of flat cart is equal to zero. Hence, the initial acceleration becomes 
. It means, option (a) 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 
and the cart exerts an accelerating force on sand particles which is also equal to 
It means the only external force or the only resultant force acting on the system is equal to 
It means the momentum of the system at any instant 
will be equal to impulse of the force 
. Hence, option (d) 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 the loaded cart at an instant will be less than the work done by the force 
up to that instant. Hence, option (c) is incorrect
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