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Question

Two masses M and m are connected at the two ends of an inextensible string. The string passes over a smooth frictionless pulley. What is the acceleration of masses and tension in the string if M is smaller then m?

A
(Mm)g
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B
mg
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C
2mMgm+M
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D
(mM)mg
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Solution

The correct option is C 2mMgm+M

m is greater than M so m will go down wards with an acceleration a. Tension on both sides of the pully will be same. Let it be T. Let us consider forces towards mass m. Here downward force is

=mgT

it is also equal to ma

therefore,

mgT=ma----- (1)

on the other side M is moving upwards so upwards force=TMg it is also equal to Ma so

TMg=Ma ------(2) from (1) and (2)

mgMg=ma+Ma

or,a=(mM)g/(m+M)

also from (1) and (2)

T=2mMg/(m+M)

Hence,

option (C) is correct answer.


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