The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is __________ m/s. Assume pulley is massless and string is light and inextensible. (Take g = 10 m/s ^2 )

Step-by-step solution

Let the acceleration of the system be a and the tension in the string be T . The equations of motion for the two masses are: 6g - T = 6a T - 2g = 2a Adding the two equations, we get: 4g = 8a a = 4g 8 = g 2 Substituting g = 10 m/s ^2 , the acceleration is: a = 10 2 = 5 m/s ^2 The 6 kg mass is released from rest ( u = 0 ) and travels a downward distance s = 6 m . Using the kinematic equation v^2 = u^2 + 2as : v^2 = 0 + 2 5 6 v^2 = 60 v = 60 7.74 m/s Answer: 7.74