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Question

In the situation given, all surfaces are frictionless. If F=Mg2, the ratio of accelerations of blocks A and B is n5. Find the value of n. (Both the blocks have mass M)


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Solution

Step 1: Given Data

Mass of the blocks =M

Given that force F=Mg2

Let the acceleration of block A be a1.

Let the acceleration of block B be a2.

a1a2=n5

Step 2: Acceleration of Block A

The force applied is acting against the motion of the block.

For block A the equation of motion can be written as,

F-Ma1=Ma1

Mg2=2Ma1

a1=g4

Step 3: Acceleration of Block B

Similarly, force applied is against the weight of the block.

For block B the equation of motion can be written as,

FMg=Ma2

Mg2-Mg=Ma2

-Mg2=Ma2

a2=-g2

Hence, a2 is in a downward direction.

Step 4: Ratio of the Accelerations

Therefore, the ratio of the accelerations are,

a1a2=n5

g4-g2=n5

12=n5

n=52

Hence, the value of n is 52.


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