Question

if v is the speed of trolley and sand bag if the mass is 200 kg and a sand bag of mass 10kg if its leaking sand 0.05kg/seconds find the speed of trolley when total sand empty​

Answer 1

Correct Question :

A trolley of mass 200 kg carrying a sandbag of 10 kg is moving uniformly with a speed of 27 km/hr 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 kg/second. What is the speed of the trolley after the entire sandbag is empty?

Given :

Mass of the trolley = 200 kg

Mass of the sand bag = 10 kg

Initial velocity = 27 km/hr

To Find :

Final velocity of trolley when total the entire sand bag is empty$.$

Solution :

❖ Since no external horizontal force acts on the whole system, linear momentum is conserved throughout the motion.

• We know that it is measured as the product of mass and velocity.

Initial momentum (p) = (M + m) u

Final momentum (p') = M v [∵ m = 0]

» M denotes mass of trolley

» m denotes mass of sand bag

Initial velocity = 27 km/hr = 7.5 m/s

By substituting the given values;

➙ (M + m) u = M v

➙ (200 + 10) × 7.5 = 200 v

➙ 210 × 7.5 = 200 v

➙ v = 1575/200

➙ v = 7.88 m/s

Answer 2

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• Initial momentum (p) = (M + m) u
• Final momentum (p') = M v

Initial velocity = 27 km/hr = 7.5 m/s.

→ (M + m) u = M v

→ (200 + 10) × 7.5 = 200 v

→ 210 × 7.5 = 200 v

→ v = 1575/200

→ v = 7.88 m/s Ans.