Question

The length of a simple pendulum is 1 m. The bob is given a velocity $7m{s}^{-1}$ in a horizontal direction from near position. During upward motion of bob, if the string breaks when it is horizontal, then the maximum vertical height of an ascent of bob from rest position is

• A. 2.5 m
• B. 2 m
• C. 3 m
• D. 3.5 m

Answer 1

The correct option is A 2.5 m

The length of the pendulum, $l=1m$

When the bob is horizontal, the height reached, $h=l$

Using conservation of energy,

Energy at the lowest point $=$ Energy at horizontal point

$⟹\frac{1}{2}m{v}_L^2=mgh+\frac{1}{2}m{v}_h^2$

$⟹v_L^2=2gl+v_h^2$

$⟹v_h^2=v_L^2-2gl$

Using equation of motion,

$v^2=u^2-2gs$

$⟹0=v_h^2-2gs$

$⟹s=\frac{v_L^2-2gl}{2g}=\frac{7^2-2\times 10\times 1}{2\times 10}=1.5m$

Therefore, the maximum vertical height $=h+s=1+1.5=2.5m$