Question

Two boats of masses 400 kg and 500 kg are connected
by a long rope. A boy of mass 50 kg in the first boat
pulls other boat by means of a rope with a force of 950
N. With what acceleration does the centre of mass of
the system of boats move?
1) 0 2) 1m/sa 3) 2m/s2 4) 0.5m/s2​

Answer 1

Given info : Two boats of masses 400 kg and 500 kg are connected by a long rope. A boy of mass 50 kg in the first boat pulls other boat by means of a rope with a force of 950N.

To find : acceleration of centre of mass of system of boats is ..

solution : force exerted by boy to 2nd boat, F₂ = 950 N

mass of 2nd boat, m₂ = 500 kg

so, acceleration of 2nd boat, a₂ = F₂/m₂ = 950/500 = 1.9 m/s²

as there is no external force acting on the system of boats and boy, so net force = 0

⇒force acting on 1st boat + force acting on 2nd boat = 0

⇒F₁ + 950 N = 0

⇒F₁ = -950 N

⇒m₁a₁ = -950 N

⇒(400kg + 50kg) × a₁ = -950 N

⇒a₁ = -950/450 = -2.1 m/s²

acceleration of centre of mass = relative acceleration= a₂ - a₁

= 1.9 - (-2.1) = 4 m/s²

Therefore the acceleration of centre of mass of system of boats and boy is 4 m/s².