$A$ demonstration apparatus on a table in the lab is shown in the diagram. It consists of a metal track (shown as a thick solid line in the figure) along which a perfectly spherical marble can roll without slipping. In one run,the marble is released from rest at a height $h$ above the table on the left section,rolls down one side and then up the other side without slipping,briefly stopping when it has reached $h_1$. Assuming the table to be horizontal and neglecting air drag as well as any energy loss due to rolling,which of the following is true?

  • A
    $h_1 < h$ always,because the friction that keeps the ball rolling must dissipate energy.
  • B
    $h_1 = h$,since total mechanical energy is conserved.
  • C
    $h_1 = h$ only if tilt angles $\phi$ and $\theta$ are equal.
  • D
    $h_1 = h$ only if tilt angle $\phi$ is larger than $\theta$.

Explore More

Similar Questions

$A$ body of mass $2 \, kg$ is projected vertically upwards with a kinetic energy of $490 \, J$. At what height will its kinetic energy become half of its initial value? $(g = 9.8 \, m/s^2)$

Difficult
View Solution

$A$ body of mass $2 \,kg$ moving in $X-Y$ plane has a potential energy given by $U = (6x + 8y) \,J$. The body is at rest at the point $(3, 2) \,m$. The work done by the body to reach another position after $2 \,s$ is: (in $\,J$)

$A$ body is projected vertically upwards with an initial velocity of $7 \, m/s$. At what height will its kinetic energy become half of its initial value (in $, m$)?

$A$ ball bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce?

Difficult
View Solution

$A$ child is swinging on a swing. The minimum and maximum heights of the swing from the earth's surface are $0.75\,m$ and $2\,m$ respectively. The maximum velocity of this swing is ............. $m/s$.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo