Question

Block A and C starts from rest and moves to right with acceleration a(A)= 12t m/s² , a(C)=3m/s².Here t is in seconds.The time when block B again comes to rest is
(98 points question)

Answer 1

Answer:

The block B will come to rest it means that the velocity of block B is zero.

The Blocks A,B,C are connected with the same rope.

By considering the portions of rope , we can see that the velocity of block B depends on Blocks A and C as.

velocity of block B(in downward)= (velocity of block A)/2 −(velocity of block C)/2

[By formula of constrained relation]

We are given accelerations. so velocity will be integration wrt time of acceleration.

so,

V

a

=6t

2

+c

V

c

=3t+c

′

Here c and c` can be considered as initial velocity, these will be zero as blocks are at rest initially.

So,

V

b

=(V

a

−V

c

)/2

V

b

=(6t

2

−3t)/2

V

b

=0

0=(6t

2

−3t)/2

6t

2

−3t=0

t(6t−3)=0

t=0 or 6t−3=0

t=0 or t=1/2

Obviously Block is at rest at t=0 as given in question also XD

So at t=1/2sec block B will at rest.

Hence,

option (D) is correct answer.