First slide

Work done by Diff type of forces

Question

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

Moderate

A

10 m
B

0.1 m
C

1 m
D

0.01 m

Solution

Let the maximum compression in the spring be x. From law of conservation of energy, $mgh = \frac{1}{2} {kx}^{2}$
$10 \times 10^{- 3} \times 10 \times 10 = \frac{1}{2} \times 200 \times x^{2}$
$\Rightarrow$ $x^{2} = 10 \times 10^{- 3} = 10^{- 2}$
$\Rightarrow$ $x = \sqrt{\frac{1}{100}} = \frac{1}{10} m = 0.1 m$
Thus, compression in the spring is 0.1m.

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