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JAMB Physics 2021 Paper

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Question : 19

Total: 40

Two bodies have masses in the ratio3:1. They experience forces which impart to them, acceleration in the ratio 2:9 respectively. Find the ratio of forces the masses experienced

1:4
2:1
2:3
2:5

Solution:

Concept:

Force is the product of mass and acceleration, so compare forces using the given ratios.

Explanation:

Let the masses be

m_1

and

m_2

with ratio

3:1

.

So,

\frac{m_1}{m_2} = \frac{3}{1}

, meaning

m_1 = 3m_2

.

Let the accelerations be

a_1

and

a_2

with ratio

2:9

.

So,

\frac{a_1}{a_2} = \frac{2}{9}

, meaning

a_1 = \frac{2}{9}a_2

.

Using

F = ma

, the force ratio is:

\frac{F_1}{F_2} = \frac{m_1 a_1}{m_2 a_2} = \frac{(3m_2)\left(\frac{2}{9}a_2\right)}{m_2 a_2}

Simplifying:

\frac{F_1}{F_2} = \frac{3 \times \frac{2}{9}}{1} = \frac{6}{9} = \frac{2}{3}

.

Hence, the ratio of the forces is

2:3

.

Answer:

C.

2:3

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