First slide

Work Energy Theorem

Question

In the figure, the ball A is released from rest when the spring is unstretched. For the block of mass M to leave contact with ground at some stage, the minimum mass of A must be

Easy

A

2 M
B

M
C

M/ 2
D

4 M

Solution

Loss in gravitational P.E = Gain in elastic P.E.
${\text{mg}}x = \frac{{\text{1}}}{{\text{2}}}{\text{k}}{x^2} \Rightarrow x = \frac{{{\text{2mg}}}}{{\text{k}}}....\left( 1 \right)$
$but\;{\text{kx}} = {\text{Mg}}....\left( 2 \right)\; \Rightarrow {\text{m}} = \frac{{\text{M}}}{{\text{2}}}$

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