Question

A metre stick , of mass 400 g, is pivoted at one end displaced through an angle ${60}^{\circ }$ . The increase in its potential energy is

• A. 1 J
• B. 10 J
• C. 100 J
• D. 1000 J

Answer 1

The correct option is A

1 J

Centre of mass of a stick lies at the mid point and when the stick is displaced through an angle ${60}^{\circ }$ it rises upto height ‘h’ from the initial position.

From the figure $h=\frac{1}{2}-\frac{1}{2}cos\theta =\frac{1}{2}(1-cos\theta )$

Hence the increment in potential energy of the stick = mgh

$=mg\frac{1}{2}(1-cos\theta )=0.4\times 10\times \frac{1}{2}(1-cos{60}^{\circ })=1J$