Question

A smooth curved surface of height $10m$ is ended horizontal. A spring of force 200 ${Nm}^{-1}$ is fixed at the horizontal end as shown in figure when an object of mass $10g$ is released from the top, it travels from the top, it travel along the curved path and collides with the spring. The maximum compression in the spring is: ($g=10{ms}^{-2}$)

• A. $10m$
• B. $0.1m$
• C. $1m$
• D. $0.01m$

Answer 1

The correct option is B $0.1m$

The object starts descending the curved surface, losing its gravitational potential energy, and gaining an equal amount of kinetic energy. At the bottom most point, the object loses all its kinetic energy to obtain the spring compression potential energy.

Thus, $mgh=\frac{1}{2}m{v}^2=\frac{1}{2}k{x}_{max}^2$

$⟹x_{max}=\sqrt{\frac{2mgh}{k}}$

$=\sqrt{\frac{2\times 0.01\times 10\times 10}{200}}$

$=0.1m$