A spring is at the bottom of a frictionless incline. When a box of mass M compre

Question

A spring is at the bottom of a frictionless incline. When a box of mass M compresses the spring distance x and is released from rest, the box slides distance d up the incline (measured from where the box is at rest). Suppose a box of mass 2M is used to compress the spring distance x, and is released from rest. The distance the box will slide up the incline now will be

d/2

between d/2 and d

d

between d/2 and d/4

d/4

between d and 2d

2d

between 2d and 4d

4d

1.

d/2

2.

between d/2 and d

3.

d

4.

between d/2 and d/4

5.

d/4

6.

between d and 2d

7.

2d

8.

between 2d and 4d

9.

4d

Explanation / Answer

According to the conservation of energy, energy stored in the spring is equal to the potnetial energy of the block

( 1/2) k x2 = m g d

d = k x2 / 2 M g

if the mass of the block increases to 2M

d = k x2 / 2 (2M) g

Hence the distance of box will slide up is d/2

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