First slide

Potential energy

Question

A metre stick of mass 400 gm is pivoted at one end and it is hanging freely .If the rod is displaced through an angle 60^o. The increase in its potential energy is

Moderate

A

2 J
B

3 J
C

0J
D

1J

Solution

When the rod is displaced through an angle $θ$ its center of gravity is increased to a height BA as shown in fig.(7) Le OA=x.
$From Δ O A C, we get \frac{x}{(1 / 2)} = c o s 60^{\circ} or 2 x = \frac{1}{2} or x = \frac{1}{4} m From figure O B = \frac{1}{2} m ∴ B A = \frac{1}{2} m - x = \frac{1}{2} m - \frac{1}{4} m = \frac{1}{4} m Change in potential energy = m g \times (B A) = 0 \cdot 4 \times 10 \times (1 / 4) = 1 joule$

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