A ball falls freely from rest from a height o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $H_0 = 6.25 \ m$ be the initial height and $H_2 = 81 \ cm = 0.81 \ m$ be the height reached after the second bounce.For a ball bouncing on a h

Vedclass · Accepted Answer

$0.6$

Vedclass · Answer

(D) Let $H_0 = 6.25 \ m$ be the initial height and $H_2 = 81 \ cm = 0.81 \ m$ be the height reached after the second bounce.For a ball bouncing on a hard surface,the height reached after $n$ bounces is given by $H_n = H_0 \cdot e^{2n}$,where $e$ is the coefficient of restitution.Given $n = 2$,$H_0 = 6.25 \ m$,and $H_2 = 0.81 \ m$.Substituting the values:$0.81 = 6.25 \cdot e^{2 	imes 2}$$0.81 = 6.25 \cdot e^4$$e^4 = \frac{0.81}{6.25} = \frac{81}{625}$Taking the square root on both sides:$e^2 = \sqrt{\frac{81}{625}} = \frac{9}{25} = 0.36$Taking the square root again:$e = \sqrt{0.36} = 0.6$Thus,the coefficient of restitution is $0.6$.

$A$ ball falls freely from rest from a height of $6.25 \ m$ onto a hard horizontal surface. If the ball reaches a height of $81 \ cm$ after the second bounce from the surface,the coefficient of restitution is

Similar Questions

$A$ ball falling freely from a height of $4.9 \, m$ hits a horizontal surface. If the coefficient of restitution is $e = \frac{3}{4}$,then the ball will hit the surface for the second time after .............. $s$.

$A$ ball makes a head-on collision with another ball of twice its mass,which is initially at rest,with a velocity of $1.5 \ m/s$. If the coefficient of restitution is $0.6$,what will be their velocities after the collision?

$A$ ball is moving with speed $20 \, m/s$ collides with a smooth surface as shown in the figure. The magnitude of the change in velocity of the ball will be ........... $m/s$.

$A$ ball strikes a smooth horizontal ground at an angle of $45^o$ with the vertical. What cannot be the possible angle of its velocity with the vertical after the collision? (Assume $e \leq 1$ ).

$A$ ball is dropped from a height of $5 \ m$ on a planet. It rebounds to a height of $1.8 \ m$. What is the fraction of velocity lost by the ball?

Vedclass Test Series

Exam Paper Generator

Online Exam Module