IIT JEE , AIEEE Forum - Physics , Mechanics

knahya.4u

Question

A body of mass M slides down an inclined plane & reaches the bottom with velocity v. If a disc of same mass rolls down the same inclined plane,what will be its velocity on reaching the bottom ?

a. v

b. v /

2

c.

2/3 v

d. v / 2

johri_anshuman

Let the body be kept at height h

when body slides down

Mgh=1/2 Mv²

when disc of same mass rolls down

Mgh= 1/2 M v₁² + 1/2 Iw²
=> 1/2 Mv² = 1/2 Mv₁²+1/2(1/2 Mr²)v₁²/r²
=> v² =v₁²+1/2v₁²
=> v²=(3/2)v₁²

=>v₁=

(2/3) v

apurviitjee2008

but if a disc rolls then there must be some friction
so in the intial case also friction would have acted..........

karthik2007

Consider the first body. Let the height of the inclined plane be h.

Using conservation of energy, we get

1/2mv² = mgh.

which gives v² = 2gh - (1)

Consider the sphere. The sphere has both rotational and translational kinetic energy. Its moment of inertia about its COG is mr²/2.

Using conservation of energy again, we get:

mgh = 1/2mv'² + 1/4mv'² (using v=rw for pure rolling)

This gives 3v'² = 2v²

which gives v' =(

2/3)v.

Option C

karthik2007

ohh... looks like anshuman got the reply a few minutes ago

johri_anshuman

apurv. it is not necessary that there shud be friction. The disc can be set into rolling motion before it is set to slide down.

apurviitjee2008

ok ok silly doubt......
got it...............

vishnu_maxlevel

but even if friction does act....work done by friction in pure rolling is 0 so u can always conserve energy

vishnu_maxlevel

but even if friction does act....work done by friction in pure rolling is 0 so u can always conserve energy

vishnu_maxlevel

sry abt the double post...my bad

shubham_sachdeva

*post edited*

priyesh

hey shubham work done by friction is zero in case of pure rolling

because the bottommost point is at rest and hence friction does not act (so work done by it is zero)

naveenranchi

@ johri anshuman

even if u release the disc after setting it in pure rolling....it will not move without slipping if there is no friction...for pure rolling on the inclined plane friction must be there...what you are saying is true for a horizontal surface....

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