Question

Three identical blocks, each of mass 10kg, are pulled as shown on the horizontal frictionless surface. If the tension (F) in the rope is 30N. What is the acceleration of each block? And what are the tensions in the other ropes? (Neglect the masses of the ropes) (Ans:a=1m/s², T1=10N, T2=20N)

Answer 1

Given conditions ⇒

Force or the tension in the Rope (F) = 30 N

Since, the mass of each block is same.

∴ m₁ = m₂ = m₃ = 10 kg.

Total mass of all the three blocks(m) = m₁ + m₂ + m₃

= 10 + 10 + 10

= 30 kg .

By the Newton's second law of the motion,

Force = mass × acceleration.

∴ Acceleration = Total Force/Total Mass

⇒ a = 30/30

∴ a = 1 m/s².

Hence, the acceleration of the each block is 1 m/s².

Now, we also need to calculate the tension in the rope.

∴ Tension in First Rope (T₁) = Mass × acceleration

= 10 × 1

= 10 N.

Tension in second rope (T₂) = Mass of two blocks × acceleration.

= 20 × 1

= 20 N.

Hope it helps.