A trolley of mass $300 k g$ carrying a sand bag of $25 k g$ is moving uniformly with a speed of $27 k m / h$ on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of $0.05 k g s^{- 1}$ . What is the speed of the trolley after the entire sand bag is empty?

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Solution

Relative velocity of bag with respect to trolley is $V_{r e l a t i v e} = 0$
Rate of mass eject, $μ = 0.05 k g / s$
Thrust force on trolley, $F = μ V_{r e l a t i v e} = 0.05 \times 0 = 0$

Hence, trolley velocity will remain equal to $27 k m / h$

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A trolley of mass 300 kg carrying a sand bag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05 kgs−1. What is the speed of the trolley after the entire sand bag is empty?

Relative velocity of bag with respect to trolley is Vrelative=0Rate of mass eject, μ= 0.05 kg/s Thrust force on trolley, F=μVrelative=0.05×0=0 Hence, trolley velocity will remain equal to 27km/h

Relative velocity of bag with respect to trolley is $V_{r e l a t i v e} = 0$
Rate of mass eject, $μ = 0.05 k g / s$
Thrust force on trolley, $F = μ V_{r e l a t i v e} = 0.05 \times 0 = 0$

Hence, trolley velocity will remain equal to $27 k m / h$