A rubber ball is dropped from a height of 5 m on a plane, where the acceleration due to gravity is not shown. On bouncing, it rises to 1.8 m . The ball loses its velocity on bouncing by a factor of (α /5) . Write value of α .

Question

A rubber ball is dropped from a height of 5 m on a plane, where the acceleration due to gravity is not shown. On bouncing, it rises to 1.8 m . The ball loses its velocity on bouncing by a factor of (α /5) . Write value of α . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

According to principle of conservation of energy
Loss in potential energy = Gain in kinetic energy

m g h = \frac{1}{2} m v^{2} \Rightarrow v = 2 g h

If

h_{1}

and

h_{2}

are initial and final heights, then

v_{1} = 2 g h_{1}

and

v_{2} = 2 g h_{2}

Loss in velocity

Δ v = v_{1} - v_{2} = 2 g h_{1} - 2 g h_{2}

∴

Fractional loss in velocity

= \frac{Δ v}{v _{1}} = \frac{2 g h _{1} - 2 g h _{2}}{2 g h _{1}} = 1 - \frac{h _{2}}{h _{1}}

= 1 - \frac{1.8}{5} = 1 - 0.36 = \frac{2}{5}

Q. A rubber ball is dropped from a height of 5m on a plane, where the acceleration due to gravity is not shown. On bouncing, it rises to 1.8m . The ball loses its velocity on bouncing by a factor of 5α​ . Write value of α .

Q. A rubber ball is dropped from a height of $5 m$ on a plane, where the acceleration due to gravity is not shown. On bouncing, it rises to $1.8 m$ . The ball loses its velocity on bouncing by a factor of $\frac{α}{5}$ . Write value of $α$ .