Question

The bob of a simple pendulum of length $50$ cm is pulled to one side such that it makes an angle of ${30}^o$ with a verticle and released. If the mass of the bob is $200$ g, the kinetic energy at the mean position is ____ J. $Takeg={10ms}^{-2}$

• A. $0.19$
• B. $0.13$
• C. $0.26$
• D. $0.49$

Answer 1

The correct option is B $0.13$

Length of string attached to bob, $l=50cm$

Mass of bob, $m=200gm=0.2kg$

If the bob is making angle ${30}^{\circ }$ with verticle, then height of bob from mean position will be,

$h=l-l\cos {30}^{\circ }=50(1-\frac{\sqrt{3}}{2})=6.69$ $cm=0.0669$ $m$

Using energy conservation,

$K.E_{mean}+P.E_{mean}=K.E_{extreme}+P.E_{extreme}$

Since at extreme, velocity is zero so kinetic energy is zero and at mean potential energy is zero

$K.E_{mean}=mgh=0.2\times 10\times 0.0669=0.13$ $J$