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Question

A block of mass m slides without friction down a fixed inclined board of inclination α with the horizontal. After leaving the inclined, the block falls on a cart of mass M filled with sand as shown.
Initial height of the block above the level of the cart is h as shown. The velocity of cart when block drops on it will be

(Assume that block and cart move together, when block drops on to the cart)

A
m2ghM+m
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B
m2ghsinαM+m
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C
m2ghcosαM+m
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D
M2ghcosαM+m
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Solution

The correct option is (D) m2ghcosαM+m

byusing3rdeqofmotion

v2u2=2gh

v=2gh

Speed of block at the bottom of board is =2gh

Let common velocity of cart and block is v

Applying conservation of linear momentum in horizontal direction,


m2ghcosα=(M+m)v
v=m2ghcosαM+m
(c)


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