Exams › JEE Main › Physics

A wagon loaded with sand leaks sand through a hole in its bottom at a constant rate lambda (mass per unit time). An external force F acts on the wagon along its direction of motion. If the instantaneous velocity of the wagon is v and the initial mass of the system is m0, which equation correctly governs the wagon's motion?

1. F = m0 dv/dt + lambda v
2. F = m0 dv/dt - lambda v
3. F = (m0 - lambda*t) dv/dt
4. F = (m0 - lambda*t) dv/dt + lambda v

Correct answer: F = (m0 - lambda*t) dv/dt

Solution

Because the sand falls out with zero velocity relative to the wagon, it produces no thrust force; the governing equation is simply F = m(t) dv/dt = (m0 - lambda*t) dv/dt.

Related JEE Main Physics questions

• Which of the following has the same SI unit as impulse?
• A monkey slides downward from a tree branch with uniform acceleration. If the maximum tension the branch can withstand is 75% of the monkey’s weight, what is the least downward acceleration that will allow the monkey to descend without snapping the branch?
• A 1000 kg car is travelling at 30 m/s. The brakes are applied until it stops. If the friction force between the tyres and the road is 5000 N, how long will the car take to come to rest?
• A rocket initially ejects gas from its rear at a mass rate of 0.1 kg s⁻¹. If the exhaust speed relative to the rocket is 50 m s⁻¹ and the rocket’s mass is 2 kg, what is its acceleration in m s⁻²?
• A block of mass M rests on a rough level floor with coefficient of friction μ. A person applies a horizontal pull, but the block remains at rest. If the total contact force exerted by the floor on the block is F, then
• Which of the following types of motion on a frictionless plane surface occurs without any force acting on the body?

⚔️ Practice JEE Main Physics free + battle 1v1 →