Two masses $m_{1}$ and $m_{2}$ are experiencing the same force where $m_{1} < m_{2}$ . the ratio of their acceleration $\frac{a_{1}}{a_{2}}$ will be

$1$

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Greater than $1$

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Less than $1$

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Cannot be determined

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Solution

The correct option is B
Greater than $1$

Equilibrium of force
The system to stay in equilibrium, the forces acting on it should be in equilibrium.
The force experienced by an object can be calculated by multiplying the mass of the object by its acceleration.
The explanation for the correct option:
Option (B):
Step 1: Given information
The two masses $m_{1}$ and $m_{2}$ ,
The ratio of their acceleration $\frac{a_{1}}{a_{2}}$ .
$F_{1} = F_{2} m_{1} a_{1} = m_{2} a_{2}$
Here,
$F_{1}$ is the force experienced by mass 1.
$F_{2}$ is the force experienced by mass 2.
$m_{1}$ and $m_{2}$ are the masses of the objects.
$a_{1}$ and $a_{2}$ are the accelerations.
Step 2: To find
We have to calculate the ratio of accelerations of the objects.
Step 3: Calculation of ratio of accelerations of the objects.
Rearranging the equation to determine the ratio of accelerations of the objects.
$\frac{a_{1}}{a_{2}} = \frac{m_{2}}{m_{1}} \frac{a_{1}}{a_{2}} > 1$
Hence, the ratio of acceleration is greater than $1$ .
Therefore, option (B) is correct.

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Two masses m1 and m2 are experiencing the same force where m1<m2. the ratio of their acceleration a1a2 will be

Two masses $m_{1}$ and $m_{2}$ are experiencing the same force where $m_{1} < m_{2}$ . the ratio of their acceleration $\frac{a_{1}}{a_{2}}$ will be