Concepts Of Physics MCQ Edition [Volume 1]PhysicsRotational Mechanics
In the arrangement shown in the figure, the two identical pulleys each have a radius R and a moment of inertia I . Calculate the acceleration of the block M .
Options
- A(M - m)g M + m
- B(M - m)g M + m + I R^2
- C(M + m)g M - m + 2I R^2
- D(M - m)g M + m + 2I R^2
Correct answer
D. (M - m)g M + m + 2I R^2
Step-by-step solution
Let a be the downward acceleration of block M . Since the string is inextensible, block m will have an upward acceleration a . Let T₁ be the tension in the string attached to M , T₂ be the tension in the horizontal segment of the string between the two pulleys, and T₃ be the tension in the string attached to m . Writing the equations of motion for the two blocks: For block M : Mg - T₁ = Ma ... (i) For block m : T₃ - mg = ma ... (ii) For the two pulleys, assuming no slipping, the angular acceleration is = a R . Writ