Question

A pulley of mass $m$ is accelerating downwards with acceleration $a$. The forces acting on the pulley are its weight $mg$ acting downwards and the tension $T$ in the string acting upwards. What is the tension $T$ in terms of $m$, $g$, and $a$?

• A. T = mg + ma
• B. T = ma - mg
• C. T = mg - ma
• D. T = mg

Answer 1

Answer: (C)

T = mg - ma

Answer 2

The forces acting on the pulley are its weight $mg$ downwards and the tension $T$ upwards. According to Newton's second law, the net force is equal to mass times acceleration ($F_{net} = ma$). Taking the downward direction as positive, the net force is $mg - T$. Therefore, $mg - T = ma$. Rearranging the equation to solve for $T$: $T = mg - ma$.