Home
Class 12
PHYSICS
A uniform solid sphere of mass m and rad...

A uniform solid sphere of mass m and radius 'R' is imparted an initial velocity `v_(0)` and angular `omega_(0) = (2v_(0))/(R )` and then placed on a rough inclined plane of inclination 'theta' and coefficient of friction `mu = 2 tan theta` as shown. The time after which the sphere will start rolling without slipping is

A

`(v_(0))/(2g sin theta)`

B

`(v_(0))/(4g sin theta)`

C

`(v_(0))/(6g sin theta)`

D

`(v_(0))/(8g sin theta)`

Text Solution

Verified by Experts

The correct Answer is:
C
`N = mg cos theta`
`f_(k) = muN = 2 tan thetatmgcostheta = 2mg sin theta`
`f_(k) - mg sin theta = ma`
`2mg sintheta - mg sin theta = ma`
` therefore a = g sin theta`
Now, `tau_(cm) = I_(cm) alpha`
`f_(k)R = (2)/(5)mR^(2)alpha`
`2mg sin theta = (2)/(5)mRalpha`
`alpha = (5g sin theta)/(R )`
Where the rolling without slipping starts
`v = omegaR`
`v_(0) + at = (omega_(0) - alphat)R`
`v_(0) + g sin thetat = omega_(0) R - 5g sin thetat`
`v_(0) + 6g sin thetat = 2v_(0)`
`therefore = (v_(0))/(6g sin theta)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A sphere of mass M rolls without slipping on the inclined plane of inclination theta . What should be the minimum coefficient of friction, so that the sphere rolls down without slipping ?

A hollow sphere of mass m and radius R is rolling downdard on a rough inclined plane of inclination theta . If the coefficient of friction between the hollow sphere and incline is mu , then

A cylinder of mass m radius R is spined to a clockwise angular velocity omega_(o) and then gently placed on an inclined plane for which coefficient of friction mu = tan theta, theta is the angle of inclined plane with the horizontal. The centre of mass of cylinder will remain stationary for time

If a solid cylinder rolls without slipping on an inclined plane of inclination '0' then the minimum coefficient of friction required to support pure rolling is

A solid cylinder of mass 3 kg is placed on a rough inclined plane of inclination 30^@ . If g = 10 ms^(2) , then the minimum frictional force required for it to roll without slipping down the plane is

A solid cylinder is rolling without slipping on a plane having inclination theta and the coefficient of static friction mu_(s) . The relation between theta and mu_(s) is

A block of mass m attached with a an ideal spring of force constant k is placed on a rough inclined plane having inclination theta with the horizontal and coefficient of friction mu=1//2 tan theta , Initially the block is held stationary with the spring in its relaxed state, find the maximum extension in the spring if the block is released.

A uniform solid sphere of radius R , rolling without sliding on a horizontal surface with an angular velocity omega_(0) , meets a rough inclined plane of inclination theta = 60^@ . The sphere starts pure rolling up the plane with an angular velocity omega Find the value of omega .

A solid sphere of mass m and radius R is rolling without slipping as shown in figure. Find angular momentum of the sphere about z-axis.

A solid sphere of radius R is set into motion on a rough horizontal surface with a inear speed v_(0) in forward direction and an angular with a linear speed v_(0) in forward directioin and an angular velocity omega_(0)=v_(0)//2R in counter clockwise direction as shown in figure. If coefficient of friction mu then find a. the time after which sphere starts pure rolling, b. the linear speed of sphere when it starts rolling and c. the work down by friction over a long time.