Home
Class 11
PHYSICS
A small block oscillates back and forth ...

A small block oscillates back and forth on a smooth concave surface of radius R. Find the time period of small oscillation.

Text Solution

Verified by Experts

For the oscillation of small block on a smooth concave surface, following figure can be drawn, where R is the radius of the concave surface.

`therefore` Restoring torque `tau=-mg R "sin"theta`
As `I=mR^(2)implies tau=-mgRtheta `(since sin `theta~= theta`)
`therefore Ialpha=-mgRthetaimpliesalpha=-(mgR)/(I)theta=-omega^(2)theta`
Time period of such oscillation is
`T=2pisqrt((I)/(mgR))=2pisqrt((mR^(2))/(mgR))impliesT=2pisqrt((R)/(g))`
Promotional Banner

Similar Questions

Explore conceptually related problems

A small block oscillates back and forth on a smooth concave surface of radius 1 m . Find the time period of small oscillations.(Take g=π^2ms^(-2) )

A small block oscillates back and forth on as smooth concave surface of radius R figure. Find the time period of small oscillation.

The time period of small oscillations of mass m :-

Find time period of oscillation of the system.

A ball of radius r is made to oscillate in a bowl of radius R, find its time period of oscillation.

In the diagram shown find the time period of pendulum for small oscillations

A ring of mass m and radius r rolls without slipping on a fixed hemispherical surface of radius R as shown. The time period of small oscillations of ring is 2pisqrt((n(R-r))/(3g)) then find the value of n.

Time Period Or Period Of Oscillation

A semi cylindrical shell with negligible thickness oscillates without slipping on a horizontal surface. The time period of small oscillations is R

A spherical ball of mass m and radius r rolls without slipping on a rough concave surface of large radius R. It makes small oscillations about the lowest point. Find the time period.