Question

A solid sphere of mass M and radius R
is resting on a block of mass 2M, kept
on a smooth horizontal plane as shown
in the figure. A variable force F is acting
on the block horizontally. If the static
and kinetic friction coefficients
between the block and the sphere are
Ms and uk respectively, When does the sphere
starts sliding on the block
​

Answer 1

Answer:

Velocity of COM →v

0

Angular velocity of sphere →0

Now, f=−μmg [ f→ Frictional force ]

⇒ma=−μmg

⇒a=−μg [ a→ retarding acceleration ]

Now, torque, τ=fR=Iα [ α→ angular acc ]

⇒α=

I

fR

=

2R

5μg

[I

sphere

=

5

2MR

2

]

Now, after time

′

t

′

⇒V=v

0

+at

=v

0

−μgt⟶(1)

Let at this time, angular velocity is ω

⇒ω=ω

0

+αt [ Initial ω=0 ]

∴ω=

2R

5μgt

⟶(2)

Now, if rolling has stared v

0

−μgt=

2

5μgt

⇒t=

7μg

2v

0

Hence, the answer is

7μg

2v

0

.