Question

Apendulum bob has asped of 3 m/s at its lowest position, The pendulum is 0.5 m long.The speed of the bob, hen the length makes an angle of ${60}^o$ to the vertical ,will be (if g=10m/s)

• A. 3 m/s
• B. $\frac{1}{3}m/s$
• C. $\frac{1}{2}m/s$
• D. 2 m/s

Answer 1

The correct option is D 2 m/s

Apply energy conservation theorem,

energy at lowest position of Bob = energy , when Bob makes 60° to the vertical

$1/2mv²=1/2mv₁²+mgl(1-cos60°)$

Here v is speed at Lowest position ,$v₁$ is speed , when it makes $60°$ with vertical and l is length of pendulum .

[Actually, height of Bob , when it makes $60°$ with vertical $=l(1-cos60°)]$

$\therefore v²=v₁²+2gl(1-cos60°)$

$3²=v₁²+2\times 10\times 0.5(1-1/2)$

$9=v₁²+5$

$v₁²=4\Rightarrow v₁=2m/s$

Hence, the option $D$ is the correct answer.