Question

A light string passing over a smooth light pulley connect two blocks of masses mm₁ and m₂ (vertical) . if the acceleration of the system is g/8 , then the ratio of the masses is [AIEEE 2002] ​

Answer 1

Explanation:

Let mass of two blocks be a and b respectively and their common acceleration be acc.

Applying equation of motion, assuming b>a

bg−T=b×acc

T−ag=a×acc

Substituting value of acc as g/8 and eliminating T,

we get b:a=9:7

Answer 2

Explanation:- As the string is inextensible , both masses have the same acceleration a . Also , the pulley is massless and frictionless , hence the tension at both ends of the string is the same suppose , the mass m₂ is greater than mass m₁ , so the heavier mass m₂ is accelerating downward and the lighter mass m₁ is accelerating upwards.

Therefore , by Newton's 2nd law

• T - m₁g = m₁a _____(i)
• m₂g - T = m₂a______(ii)
• after solving equs (i) and (ii) , we get
• a = (m₂-m₁) (m₁+ m₂ )g = g/8[ given ]
• so, m₂(1-m₁/m₂)/m₂(1+m₁ /m₂) •g = g/8 ______(iii)
• Let m₁ /m₂ = x
• thus, equs (iii) becomes
• 1-x/1+x = g/8
• or ,x = 7/9 or m₂/m₁ = 9/7 Answer

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