Home
Class 11
PHYSICS
A small object of uniform density rolls ...

A small object of uniform density rolls up a curved surface with an initial velocity v. it reaches up to a maximum height of `(3v^2)/(4g)

with respect to the initial position. The object is

Text Solution

Verified by Experts

The kinetic energy of the rolling object is converted into potential energy at height `h`
`= 3v^(2)//4g`, Fig.
`:. (1)/(2)mv^(2) + (1)/(2)I omega^(2) = mgh`
`(1)/(2)mv^(2) + (1)/(2)I (v^(2))/(r^(2)) = mg ((3v^(2))/(4g)) ( :'omega = (v)/(r ))`
or `(1)/(2)I (v^(2))/(r^(2)) = (3)/(4)mv^(2) - (1)/(2)mv^(2) = (1)/(4)mv^(2)` or `I = (1)/(2)mr^(2)`
As `((1)/(2)mr^(2))` is moment of inertia of a circular disc of mass `m` and radius `r` about an axis passing through its centre and perpendicular to its plane, the object must be a circular disc.
Promotional Banner

Topper's Solved these Questions

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    PRADEEP|Exercise VALUE BASED QUESTIONS|5 Videos

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    PRADEEP|Exercise CURIOSITY QUESTIONS|4 Videos

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    PRADEEP|Exercise ADDITIONAL EXERCISES|11 Videos

  • RAY OPTICS

    PRADEEP|Exercise Problem For Practice(a)|25 Videos

  • THERMODYNAMICS

    PRADEEP|Exercise Assertion- Reason Type Questions|19 Videos

Similar Questions

Explore conceptually related problems

A small object of uniform density rolls up a curved surface with an initial velocity 'w'. It reaches up to a maximum height of (3u^(2))/(4g) with respect to initial position. The object is:

A small object of uniform density rolls up a curved surface with an initial velocity v . It reached upto maximum height of 3v^(2)//4g with respect to the initial position. The object is - .

A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of 5v2 / 6g with respect to the initial position. The object is- О. o ring O solid sphere O hollow sphere o disc

When a body thrown vertically up with an initial velocity vo ,then maximum height reached by the body is

An object of radius R and mass M is rolling horizontally without slipping with speed v . It then rolls up the hill to a maximum height h = (3v^(2))/(4g) . The moment of inertia of the object is ( g = acceleration due to gravity)

For a body thrown vertically up with an initial velocity u ,the maximum height reached by body from the ground is

When a ball is thrown up vertically with velocity v_0 , it reaches a maximum height of h. If one wishes to triple the maximum height then the ball should be thrown with velocity