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Question

In the figure shown neglecting friction and mass of pulleys, what is the acceleration of mass B?


A

g3

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B

5g2

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C

2g2

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D

2g5

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Solution

The correct option is D

2g5


Step 1: Write the Equations of Motion

Let the acceleration of mass A be aA and acceleration of mass B be aB.

Therefore, the accelerations can be expressed as,

aA=aB+02

⇒2aA=aB 1

Let, TA be the tension on the string for mass A, and g be the acceleration due to gravity.

Then the equation of motion of mass A is

mg-TA=maA

⇒mg=maA+TA 2

Similarly, the equation of motion of mass B is

TB-mg=maB

⇒mg=TB-maB

From equation 1 we get,

mg=TB-2maA

2mg=2TB-4maA

Since the mass of the pulleys can be neglected we get

TA=2TB

∴2mg=TA-4maA 3

Step 2: Solve the Equations

Upon Subtracting 2 from 3 we get

2mg-mg=TA-TA-4maA-maA

⇒mg=-5maA

Upon neglecting the negative sign we get

aA=g5

From equation 1 we get

aB=2g5

Hence, the correct answer is option (D).


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