Question

A block of mass $\sqrt{2}kg$ is released from the top of an inclined smooth surface as shown in figure.If spring constant of spring is 100 N/m and block comes to rest after compressing the spring by 1 m, then the distance travelled by block before it comes to rest is

• A. 1 m
• B. 1.25 m
• C. 2.5 m
• D. 5 m

Answer 1

Answer: (D)

5 m

Let the distance travelled by the block is $s$.

Since, the work done by the block will be equal to potential energy stored in the spring.

It is given as,

$\left(mg\sin \theta \right)\times s=\frac{1}{2}k{x}^2$

$\left(\sqrt{2}\times 10\times \sin {45}^{\circ }\right)\times s=\frac{1}{2}\times 100{\left(1\right)}^2$

$s=5m$

Thus, the distance travelled by the block is $5m$.