A block of mass ' $\mathrm{M}$ ' rests on a piston executing S.H.M. of period one second. The amplitude of…
A block of mass ' $\mathrm{M}$ ' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that the mass is separated from the piston, is
(acceleration due to gravity, $\mathrm{g}=10 \mathrm{~ms}^{-2}, \pi^2=10$ )
0.25 m
0.5 m
1 m
$\infty$
Solution
Given that, $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}=1 \mathrm{~s}$
$\therefore \quad \frac{\mathrm{m}}{\mathrm{k}}=\frac{1}{4 \pi^2}$
The block will separate, when the restoring force exceeds the force due to gravity. i.e., $\mathrm{kx} \geq \mathrm{Mg}$
$\therefore \quad \mathrm{x} \geq \frac{\mathrm{Mg}}{\mathrm{k}}=\frac{\mathrm{g}}{4 \pi^2}=\frac{10}{4 \times 10}=0.25 \mathrm{~m}$