JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2026
- Easy
- MCQ
The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M . Two blocks of mass of M and m are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in vertical plane about its centre. The magnitudes of the acceleration experienced by the blocks is _________ (assume no slipping of string on pulley.)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(\frac{( M - m ) g }{\left[\left(\frac{8}{3}\right) M + m \right]}\)
Step-by-step Solution
Detailed explanation
\(Mg - T _2= Ma\)\(\quad\)...(1)
\(T _1- mg = ma\)\(\quad\)...(2)
\(\left( T _2- T _1\right) r = I \frac{ a }{ r }\)\(\quad\)...(3)
\((1)+(2)+(3)\)
\((M-m) g=\left(M+m+\frac{I}{r^2}\right) a\)
Here \(I= Mr ^2+\frac{ M \times(2 r )^2}{12} \times 2\)
\(=\left(1+\frac{2}{3}\right) Mr ^2\)
\(=\frac{5}{3} Mr ^2\)
\((M-m) g=\left[M+m+\frac{5 M}{3}\right] a\)
\(a=\frac{(M-m) g}{\left[M+m+\frac{5 M}{3}\right]}\)
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