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A block of mass M, with a semicircular t...

A block of mass M, with a semicircular track of radius R rest on a horizontal frictionless surface. A uniform cylinder of radius r and mass m is released from rest at the point of the semicircular track. The cylinder slips in the semicircular frictionless track. How far the block moved when the cylinder reaches the bottom of the track ?

Text Solution

Verified by Experts

The correct Answer is:
`(m)/(M+m)(R-r)`
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A block of mass M with a semi circular track of radius R, rests on a horizontal frictionless surface. A uniform cylinder of radius r and mass m is released from rest at the top point A. The cylinder slips on the semicurcular frictionless track. How far has the block moved when the cylinder reaches the bottom of the track ? How fast is the block moving when the cylinder reaches the bottom of the track ?

A block of mass M with a semicircualr of radius R, rests on a horizontal frictionless surface. A uniform cylinder of radius r and mass m is released from rest the top point A The cylinder slips on the semicircular frictionless track. How far has the block moved when the cylinder reaches the bottom (point B) of the track ? How fast is the block moving when the cylinder reaches the bottom of the track?

Knowledge Check

  • A block of mass M = 2 kg with a semicircular track of radius R = 1.1 m rests on a horizontal frictionless surface. A uniform cylinder of radius r = 10 cm and mass = 1.0 kg is released from rest from the top point A. the cylinder slips on the semicircular frictionless track. The speed of the block when the cylinder reaches the bottom of the track at B is (g =10ms^(-2))

    A
    `sqrt((10)/(3))ms^(-1)`
    B
    `sqrt((4)/(3))ms^(-1)`
    C
    `sqrt((5)/(2))ms^(-1)`
    D
    `sqrt(10)ms^(-1)`

  • A solid cylinder of radius 0.35 m is released from rest from a height of 1.8 m and rolls down the incline as shown in the figure. What is the angular speed of the cylinder when it reaches the horizontal surface?

    A
    8.2 rad/s
    B
    34 rad/s
    C
    14 rad/s
    D
    67 rad/s

  • A uniform solid cylinder of mass 2 kg and radius 0.2 m is released from rest at the top of a semicircular track of radius 0.7 m cut in a block of mass M = 3 kg as shown in Fig. The block is resting on a smooth horizontal surface and the cylinder rolls down without slipping. Based on the above information, answer the following questions: The speed of the point of contact of the cylinder with the block w.r.t. ground, when the cylinder reaches the bottom of the track is

    A
    `2/(sqrt(11))m//s`
    B
    `8/(sqrt(11))m//s`
    C
    `4/(sqrt(11))m//s`
    D
    `6/(sqrt(11))m//s`

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