Question

A partical of mass, m moving under a constant force F convers x1 displacement in first n seconds and x2 displacement in next n seconds. If the initial velocity of the particle is 0, then the value of n is -

Answer 1

Given :

Mass of the particle = m

Applied force = F

Particle covers x₁ displacement in first n seconds and x₂ displacement in next n seconds.

Initial velocity = zero.

To Find :

Value of n

Solution :

❖ First of all we need to find acceleration of the body. It can be calculated by using the relation between force and acceleration$.$

➙ Force = Mass × Acceleration

➙ F = m × a

➙ a = F/m

A] Distance covered in first n seconds :

➙ x₁ = un + 1/2 an²

➙ x₁ = 0 + 1/2 (F/m) n²

➙ x₁ = Fn²/2m .......... (I)

B] Distance covered in next n seconds :

Here we can say that, body covers (x₁ + x₂) distance in 2n seconds.

➙ (x₁ + x₂) = u(2n) + 1/2 a(2n)²

➙ (x₁ + x₂) = 0 + 1/2 (F/m) (4n²)

➙ x₁ + x₂ = 4Fn²/2m

➙ x₁ + x₂ = 2Fn²/m .......... (II)

From the (II) equations,

➛ x₁ + x₂ = 2Fn²/m

➛ m (x₁ + x₂) = 2Fn²

➛ n² = m (x₁ + x₂) / 2F

➛ n = √m (x₁ + x₂) / 2F

∴ (C) is the correct answer!

Answer 2

Answer:

Given :

Mass of the particle = m

Applied force = F

Particle covers x₁ displacement in first n seconds and x₂ displacement in next n seconds.

Initial velocity = zero.

To Find :

Value of n

Solution :

❖ First of all we need to find acceleration of the body. It can be calculated by using the relation between force and acceleration..

➙ Force = Mass × Acceleration

➙ F = m × a

➙ a = F/m

A] Distance covered in first n seconds :

➙ x₁ = un + 1/2 an²

➙ x₁ = 0 + 1/2 (F/m) n²

➙ x₁ = Fn²/2m .......... (I)

B] Distance covered in next n seconds :

Here we can say that, body covers (x₁ + x₂) distance in 2n seconds.

➙ (x₁ + x₂) = u(2n) + 1/2 a(2n)²

➙ (x₁ + x₂) = 0 + 1/2 (F/m) (4n²)

➙ x₁ + x₂ = 4Fn²/2m

➙ x₁ + x₂ = 2Fn²/m .......... (II)

From the (II) equations,

➛ x₁ + x₂ = 2Fn²/m

➛ m (x₁ + x₂) = 2Fn²

➛ n² = m (x₁ + x₂) / 2F

➛ n = √m (x₁ + x₂) / 2F

∴ (C) is the correct answer!