Two monkeys M1 and M2 of equal mass ' m ' can climb strings of a pulley arrangement as shown in figure. Find magnitude of acceleration (in m / s 2 ) of M1 with respect to rope so that block remains stationary. It is given that M2 is just holding the string. Assume pulley is frictionless and string is massless and inextensible.

Question

Two monkeys M1 and M2 of equal mass ' m ' can climb strings of a pulley arrangement as shown in figure. Find magnitude of acceleration (in m / s 2 ) of M1 with respect to rope so that block remains stationary. It is given that M2 is just holding the string. Assume pulley is frictionless and string is massless and inextensible. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

T=5 m g a2=(5 m g-m g/m)=4 g T'=2 T=10 mg a1=(10 m g-m g/m)=9 g Acceleration of the rope is equal to the acceleration of the moving pulley. Hence acceleration of M1 with respect to rope aM1, textRope =9 g-(-2 g)=11 g=110 m / s 2

T=5mg a2​=m5mg−mg​=4g T′=2T=10mg a1​=m10mg−mg​=9g Acceleration of the rope is equal to the acceleration of the moving pulley. Hence acceleration of M1​ with respect to rope aM1​,Rope​=9g−(−2g)=11g=110m/s2

$T = 5 m g$
$a_{2} = \frac{5 m g - m g}{m} = 4 g$
$T^{'} = 2 T = 10 m g$
$a_{1} = \frac{10 m g - m g}{m} = 9 g$
Acceleration of the rope is equal to the acceleration of the moving pulley.
Hence acceleration of $M_{1}$ with respect to rope
$a_{M_{1}, Rope} = 9 g - (- 2 g) = 11 g = 110 m / s^{2}$