A body falls from a height h on a horizontal surface and rebounds. Then it falls again and rebounds and so on. If the restitution coefficient is $\frac{1}{3}$ , the total distance covered by the body before it comes to rest is

$\frac{h}{4}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{5 h}{4}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$2 h$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$3 h$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
$\frac{5 h}{4}$

Total distance travelled is given by $s = h + 2 e^{2} h + 2 e^{4} h + \dots \dots$
$= h + 2 e^{2} h (1 + e^{2} + e^{4} + \dots \dots) = h + \frac{2 e^{2} h}{1 - e^{2}} = h (\frac{1 + e^{2}}{1 - e^{2}}) = h ⎡ ⎣ \frac{1 + {(\frac{1}{3})}^{2}}{1 - {(\frac{1}{3})}^{2}} ⎤ ⎦ = \frac{5 h}{4}$
Hence, the correct choice is (b).

Suggest Corrections

Similar questions

Q. A body falls from a height 'h' on a horizontal surface and rebounds. Then it falls again and again rebounds and so on. If the restitution coefficient is

\frac{1}{3}

, the total distance covered by the body before it comes to rest is

Q. A body falls from a height h on a horizontal surface and rebounds. Then it falls again and again rebounds and so on. If the restitution coefficients is

\frac{1}{3}

, the total distance covered by the body before it comes to rest is

A body falls from a height h on a horizontal surface and rebounds. Then it falls again and rebounds and so on. If the restitution coefficient is $\frac{1}{3}$ , the total distance covered by the body before it comes to rest is

Q. A body falls from a height 'h' on a horizontal surface and rebounds. Then it falls again and again rebounds and so on. If the restitution coefficient is

\frac{1}{3}

, the total time taken by the body to come to rest is

Q. A body falls from a height '$h$' on a horizontal surface and rebounds. Then it falls again and rebounds and so on. If the coefficient of restitution is $\dfrac{1}{2}$, then the total distance travelled by the ball before coming to rest is (neglect air resistance)

Join BYJU'S Learning Program

A body falls from a height h on a horizontal surface and rebounds. Then it falls again and rebounds and so on. If the restitution coefficient is 13, the total distance covered by the body before it comes to rest is

The correct option is B 5h4 Total distance travelled is given by s=h+2e2h+2e4h+…… =h+2e2h(1+e2+e4+……)=h+2e2h1−e2=h(1+e21−e2)=h⎡⎣1+(13)21−(13)2⎤⎦=5h4 Hence, the correct choice is (b).

A body falls from a height h on a horizontal surface and rebounds. Then it falls again and rebounds and so on. If the restitution coefficient is $\frac{1}{3}$ , the total distance covered by the body before it comes to rest is