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

A small block oscillates back and forth on as smooth concave surface of radius R in figure. 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) )

The time period of small oscillations of mass m :-

The ear ring of a lady shown in figure has a 3 cm long light suspension wire. A. Find the time period of small oscillations if the lady is standing on the ground. b. The lady now sits in a merry go round moving at 4ms^-1 in a circle of radius 2 m. find the time period of small oscillation of the ear ring.

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.

A solid uniform cylinder of mass m performs small oscillations due to the action of two springs of stiffness k each (figure). Find the period of these oscillation in the absence of sliding. x

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.

A small block of mass m is placed at the bottom of fixed circular smooth surface of radius R as shown in the figure If a velocity v. 14 gR is given to the block then maximum height from the bottom of circular surface, where block will leave the contact

Statement I: A circular metal hop is suspended on the edge by a hook. the hoop can oscillate side to side in the plane of the hoop, or it can oscillate back and forth in a direction perpendicular to the plane of the hoop. The time period of oscillation would be more when oscillation are carried out in the plane of hoop. Statement II: Time period of physical pendulum is more if moment of inertial of the rigid body about corresponding axis passing through the pivoted point is more.

A system is shown in the figure. The force The time period for small oscillations of the two blocks will be

A solid sphere (radius = R) rolls without slipping in a cylindrical throuh (radius = 5R) . Findthe time period of small oscillations.