Question

A block of mass 2 kg is placed on a rough inclined plane as shown in figure ($\mu =0.2$) so that it just touches the spring. The block is allowed to move downwards. The spring will be compressed to a maximum of

• A. 0.1 cm
• B. 6.6 m
• C. 1 cm
• D. 13 cm

Answer 1

The correct option is D 13 cm

The block keeps moving till its velocity becomes 0 again.

No KE, implies, total work done by all forces = 0

Work done by gravity + friction = Work done on spring $(W_{Normal}=0)$

$mgsin\theta x-\mu mgcos\theta x=0.5k{x}^2$

$x=2mg(sin\theta -\mu cos\theta )/k=$ 2(2x10)(1/2 - 0.2$\sqrt{3}$/2)/100

$x=13cm$