Question

Two blocks of mass $m=5$kg and $M=10$kg are connected by a string passing over a pulley B as shown. Another string connects the center of pulley B to the floor and passes over another pulley A as shown. An upward force F is applied at the center of pulley A. Both the pulleys are massless. Find the acceleration of blocks m and M (in $m/s^2$) if F is 500 N

• A. 5, 0
• B. 2.5, 5
• C. 5, 7.5
• D. 15, 2.5

Answer 1

The correct option is D 15, 2.5

The gravitational force on mass m , $F_m=mg=50N$ and force on M, $F_M=Mg=100N$. Given $F=500N$ . So $\frac{F}{4}=125N$ is greater than the forces 50 N and 100 N . This is enough force to move the both of masses through the pulley. The acceleration of masses, $a_m=\frac{125-50}{5}=15m/s^2$ and $a_M=\frac{125-100}{10}=2.5m/s^2$.