Three weightless pulleys with radii R, 2R and 3R are concentrically fastened together to make a single triple pulley system and mounted on an axis on which the triple pulley can rotate without friction (figure). The threads are light and they do not slip on the pulley. We suspended masses 8m, m and 2m as shown. What is the acceleration $(i n m / s^{2})$ of mass 8m ? $(g = 10 m / s^{2})$

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

answer is 4.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

A system of pullies is massless, ${(τ_{n e t})}_{0} = 0$

$T_{1} R + T_{3} (3 R) - T_{2} (2 R) = 0 T_{1} + 3 T_{3} = 2 T_{2}____________(1) 8 m g - T_{1} = 8 m (R α) T_{1} = 8 m (g - R α)_________(2) S i m i l a r l y, T_{3} = 2 m (g - 3 R α)_________(3) T_{2} = m (g + 2 R α)_________(4)$

Substituting (2), (3), (4) in (1)
$8 m (g - R α) + 6 m (g - 3 R α) = 2 m (g + 2 R α)$
$12 g = 30 R α \Rightarrow R α = \frac{12 g}{30} = \frac{120}{30} = 4 m s^{- 2}$