In the arrangement shown in the figure, the pulley has a mass 3m, Neglecting friction on the contact surface, the force exerted by the supporting rope AB on the ceiling is

Options

A. 6 mg
B. 3 mg
C. 4 mg
D. None of the above

Answer

D

Explanation

(d) Acceleration of system,
`a=(" Net pulling force")/(" Total mass")`
`=(2mg=mg)/(3m)=(g)/(3)`
Now from equation of motion of m
`T-mg=ma=(mg)/(3)`
`therefore T=(4mg)/(3)`
For equilibrium of pulley,
`T_(AB)=2T+` weight of pulley
`=(8mg)/(3)+3mg=(17 mg)/(3)`