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A cylinder and a block are at the top of an inclined ramp. The cylinder rolls down the ramp without slipping; the block falls vertically without friction at the same instant. (a) Which object reaches the bottom first? (A) The cylinder (B) The block (C) They arrive at the same time. (D) There is not enough information to answer the question. (b) Which object reaches the bottom with the larger speed? (A) The cylinder (B) The block (C) They arrive with the same speed. (D) There is not enough information to answer the question. (c) Which object experiences the larger acceleration? (A) Cylinder A (B) Block B (C) They experience the same acceleration. (D) There is not enough information to answer the question

A cylinder and a block are at the top of an inclined ramp. The cylinder rolls down the ramp without slipping; the block falls vertically without friction at the same instant.
(a) Which object reaches the bottom first?
(A) The cylinder (B) The block
(C) They arrive at the same time.
(D) There is not enough information to answer the question.
(b) Which object reaches the bottom with the larger speed? (A) The cylinder (B) The block
(C) They arrive with the same speed.
(D) There is not enough information to answer the question.
(c) Which object experiences the larger acceleration? (A) Cylinder A (B) Block B
(C) They experience the same acceleration.
(D) There is not enough information to answer the question   

Grade:11

2 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
(a) The correct option is (B) the block.
A cylinder and a block are at the top of an inclined ramp. The cylinder rolls down the ramp without slipping and the block falls vertically without friction at the same instant. The acceleration of the cylinder will be gsinθ (θ is the angle of inclined plane with horizontal), whereas the acceleration the ball when it fall along the vertically will be equal to acceleration due to gravity g. The value of sinθ lies between 0 to 1. Therefore the acceleration will greater in the case of the block than the cylinder. Thus the block reaches the bottom first. From the above observation we conclude that, option (B) is correct.
(b) The correct option is (B) the block.
As the block reaches the bottom first, therefore the block reaches the bottom with the larger speed. Thus option (B) is correct.
(c) The correct option is (B) the block.
The acceleration of the cylinder will be gsinθ (θ is the angle of inclined plane with horizontal), whereas the acceleration the ball when it fall along the vertically will be equal to acceleration due to gravity g. The value of sinθ lies between 0 to 1. Therefore the acceleration will greater in the case of the block than the cylinder. From the above observation we conclude that, option (B) is correct.

Hasan Naqvi
97 Points
8 years ago
(a) The correct option is (B) the block.
 
(b) The correct option is (C) they both have same speed.
The acceleration of block is g, and distance covered by it h.
The acceleration of cylinder is gsinθ and distance covered by it h.cosecθ
 
We know v2-u2 = 2as, as the product of acceleration and distance is same for both the block and cylinder, final velocity of both will be same.
 
(c) The correct option is (B) the block.

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