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Question: A metre stick, of mass 400 g, is pivoted at one end displaced through an angle \(60 ^ { \circ }\). T...

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

A

1 J

B

10 J

C

100 J

D

1000 J

Answer

1 J

Explanation

Solution

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

From the figure h=l2−l2cos⁡θh = \frac { l } { 2 } - \frac { l } { 2 } \cos \theta =l2(1−cos⁡θ)= \frac { l } { 2 } ( 1 - \cos \theta )

Hence the increment in potential energy of the stick = mgh

=mgl2(1−cos⁡θ)=0.4×10×12(1−cos⁡60∘)=1J= m g \frac { l } { 2 } ( 1 - \cos \theta ) = 0.4 \times 10 \times \frac { 1 } { 2 } \left( 1 - \cos 60 ^ { \circ } \right) = 1 J