Question

A force of 10N produces an acceleration of 2m/s on a
mass m1 and an acceleration of 5m/s2 on a mass m2.
What acceleration would the same force provide if both
the masses are tied together?
6m/s2
FO
12m/s2
1.4m/s2
5m/s2​

Answer 1

Answer :-

When the masses are tied together, the force would provide an acceleration of 1.4 m/s² .

Explanation :-

For mass 'm₁' :-

• Force (F) = 10 N

• Acceleration (a₁) = 2 m/s²

By Newton's 2nd law of motion :-

F = m₁a₁

⇒ 10 = m₁(2)

⇒ m₁ = 10/2

⇒ m₁ = 5 kg

For mass 'm₂' :-

• Force (F) = 10 N

• Acceleration (a₂) = 5 m/s²

F = m₂a₂

⇒ 10 = m₂(5)

⇒ m₂ = 10/5

⇒ m₂ = 2 kg

When masses are tied together :-

• Force = 10 N

• Mass = m₁ + m₂

F = a[m₁ + m₂]

⇒ 10 = a[5 + 2]

⇒ 10 = 7a

⇒ a = 10/7

⇒ a = 1.4 m/s²

Answer 2

Given :-

A  force of 10N produces an acceleration of 2m/s² on a  mass m1 and an acceleration of 5m/s² on a mass m2.

To Find :-

Total mass

Solution :-

Let the force be f and f'

f = f'

10 = 10

ma = m₂a₂

m(2) = m₂(5)

2m = 5m₂

Solving both one by one

2m = 10

m = 10/2

m = 5 kg

For m₂

5m₂ = 10

m₂ = 10/5

m₂ = 2 kg

Now

The total mass = 5 + 2 = 7 kg

f = ma

10 = a(7)

10 = 7a

10/7 = a

1.4 = a

$\sf Acceleration = 1.4 \; m/s^2$