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Question

Two blocks of equal mass 'm' are connected by massless string and pulley as shown in figure. Now the blocks are left to move. Then the force exerted by pulley on the clamp is 33mgk. Find the value k?
1032495_e44252fbcafe4683844b43b89d69c5ae.png

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Solution

Let the acceleration of blocks =a
from (1)
mgT=ma
For (2)
Tmgsin30=ma
Tmgsin30=mgT
2T=mg+mgsin30=32mg
T=34mg

Now FBD of clamp with, pully [ref image 2]
Now force exerted by pully on clamp = resultant of the two tension [Ref. image 2]

Fresut=T2+T2+2×T×T×cos60

=3T

F=33mg4

k=4

1459314_1032495_ans_721396690a604c55a49c8bc9f803d5a2.png

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