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The ratio of the acceleration for a soli...

The ratio of the acceleration for a solid sphere (mass m and radius R ) rolling down an incline of angle `theta` without slipping and slipping down the incline without rolling is

A

`5 : 7 `

B

`2 : 3 `

C

`2 : 5 `

D

`7 : 5 `

Text Solution

Verified by Experts

The correct Answer is:
A
`a_("slipping") = g sin theta , a_("rolling") = (g sin theta)/(1 + (k^(2))/(r^(2)))`
For sphere,` k = sqrt((2)/(5))r " " therefore k^(2) = (2)/(5) r^(2)`
So, ` a_("rolling") = (g sin theta)/( 1 + (2)/(5)) = (5)/(7) g sin theta`
`therefore (a_("rolling"))/(a_("slipping")) = ((5)/(7) g sin theta)/(g sin theta) = (5)/(7)`
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Knowledge Check

  • The ratio of the accelerations for a solid sphere (mass 'm' and radius 'R') rolling down an incline of angle theta without slipping and slipping down the incline without rolling is

    A
    `5:7`
    B
    `2:3`
    C
    `2:5`
    D
    `7:5`

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    A
    42 J
    B
    60 J
    C
    36 J
    D
    70 J

  • A uniform rod of mass mis supported on two rolles each of mass m/2 and radius r and rolls down the inclined rough plane as shown in the figure. Assuming no slipping at any contact and treating the rollers as uniform solid cylinders. Answer the following question based on above Passage: If the friction force on roller at the contact point with incline is f_1 and at the contact point with rod is f_2 then :

    A
    `f_1 gt f_2`
    B
    `f_1 lt f_2`
    C
    `f_1 = f_2`
    D
    data is insufficient to decide

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