A solid cylinder of mass M and radius R ...

A solid cylinder of mass M and radius R rolls down an inclined plane of height h. The angular velocity of the cylinder when it reaches the bottom of the plane will be :

`(1)/(R ) sqrt((gh )/(2))`

`(2)/(R ) sqrt((gh )/(3))`

`(1)/(R ) sqrt((2gh )/(3))`

`(3)/(R ) sqrt((gh )/(2))`

Text Solution

Verified by Experts

The correct Answer is:

`I=(1) /(2) MR^(2)`
when the cylinder rails down the inclined plane from a vertical height h its potential energy Mgh is partly convered into translations kinetic energy `(1)/(2) Mv ^(2)` and partly into rotational kinetic energy `(1)/(2) lomega ^(2)` . therefore
`Mgh =(1)/(2) Mv ^(2) +(1)(2) l omega ^(2)`
`= (1)/(2) mv^(2) + (1)/(2) ((1)/(2) Mr^(2) MR ^(2)) omega ^(2) `
`=(1)/(2) M ( R omega )^(2) + (1)/(2) MR ^(2) omega ^(2) ( :' R omega )`
`Mgh =(3)/(4) MR ^(2) omega ^(2)`
`oemga = sqrt((4gh )/( 3R ^(2)))=(2)/(R)sqrt((gh)/(3))`

Topper's Solved these Questions

NEET DRILL TEST 5
NEET MAJOR TEST (COACHING)|Exercise PHYSICS|45 Videos
NEET MAJOR TEST 9
NEET MAJOR TEST (COACHING)|Exercise PHYSICS|45 Videos

Assertion: A solid cylinder of mass m and radius r rolls down an inclined plane of height H. The rotational kinetic energy of the cylinder when it reaches the bottom of the plane is mgH/3. Reason: The total energy of the cylinder remains constant throughout its motion.

Assertion is True, Reason is True, Reason is a correct explanation for Assertion

Assertion is True, Reason is True, Reason is not a correct explanation for Assertion

Assertion is True, Reason is False

Assertion is False but, Reason is True.

A solid cylinder rolls down from an inclined plane of height h. What is the velocity of the cylinder when it reaches at the bottom of the plane ?

`sqrt((2gh)/3)`

`sqrt(2gh)`

`sqrt((4gh)/3)`

`sqrt((3gh)/2)`

A solid cylinder rolls without slipping down an inclined plane of height h. The velocity of the cylinder when it reaches the bouom is

`sqrt((2gh)/(3))`

`sqrt((4gh)/(3))`

`sqrt((3gh)/(2))`

`sqrt(gh)`