First slide

Motion of centre of mass

Question

Two blocks of masses m and 2m are kept on a smooth horizontal surface. They are connected by an ideal spring of force constant k. Initially, the spring is unstretched. A constant force is applied to the heavier block in the direction as shown in figure. Suppose at time t, displacement of smaller block is x, then displacement of the heavier block at this moment would be

Moderate

A

$\frac{x}{2}$
B

$\frac{{Ft}^{2}}{6 m} + \frac{x}{3}$
C

$\frac{x}{3}$
D

$\frac{{Ft}^{2}}{4 m} - \frac{x}{2}$

Solution

$X_{CM} = \frac{m x + 2 m x_{2 m}}{m + 2 m}$
$∴ \frac{1}{2} a_{CM} t^{2} = \frac{x + 2 x_{2 m}}{3}$
$∴ \frac{3}{2} (\frac{F}{3 m}) t^{2} = x + 2 x_{2 m}$ $[∵ F = {Ma}_{CM}]$
$∴ x_{2 m} = \frac{{Ft}^{2}}{4 m} - \frac{x}{2}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App