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# Find the values of ${F_1}$ and ${a_2}$ in the table given below.Mass $m{\text{ (kg)}}$Acceleration $a{\text{ (m/}}{{\text{s}}^2}{\text{)}}$ Force $F{\text{ (N)}}$251.2${F_1}$1.5${a_2}$2.25A) 15, 1.2B) 1.5, 20C) 25, 1.5D) 30, 1.5

Last updated date: 14th Apr 2024
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Hint: Use Newton’ s second law of motion which gives force as the product of mass and acceleration to find ${F_1}$ and ${a_2}$

Formula Used: Force $F$ acting on a body of mass $m$to provide an acceleration $a$ to it is given by, $F = ma$

Step 1: List the information provided in the first row of the table
From the first row of the table we have,
Mass of the body, ${m_1} = 25{\text{kg}}$
Acceleration of the body, ${a_1} = 1.2{\text{m/}}{{\text{s}}^2}$
Force ${F_1}$ of the body is unknown
Step 2: Use the force equation $F = ma$ to find ${F_1}$
From the force equation we have ${F_1} = ma$
Substituting the values of ${m_1} = 25{\text{kg}}$ and ${a_1} = 1.2{\text{m/}}{{\text{s}}^2}$ in the above equation
Then, we have ${F_1} = 25 \times 1.2 = 30{\text{N}}$
i.e., the force applied on a body of mass of ${\text{25kg}}$ to produce an acceleration of ${\text{1}}{\text{.2m/}}{{\text{s}}^2}$ is ${\text{30N}}$

Step 3: List the information provided in the second row of the table
From the second row of the table we have,
Mass of the body, ${m_2} = 1.5{\text{kg}}$
Force applied on the body, ${F_2} = 2.25{\text{N}}$
Acceleration ${a_2}$of the body is unknown
Step 4: Use the force equation $F = ma$ to find ${a_2}$
From the force equation we have ${F_2} = {m_2}{a_2}$
Expressing the force equation in terms of acceleration ${a_2}$ we get, ${a_2} = \dfrac{{{F_2}}}{{{m_2}}}$
Substituting the values of ${m_2} = 1.5{\text{kg}}$ and ${F_2} = 2.25{\text{N}}$ in the above equation
Then, we have ${a_2} = \dfrac{{2.25}}{{1.5}} = 1.5{\text{m/}}{{\text{s}}^2}$
i.e., when a force of ${\text{2}}{\text{.25N}}$ is applied on a body of mass of ${\text{25kg}}$ an acceleration of ${\text{1}}{\text{.5m/}}{{\text{s}}^2}$ is produced

Therefore, the correct option is d) 30, 1.5

Note: Newton’ s second law states that the rate of change of momentum $(p)$ of a body is directly proportional to the applied force and takes place in the direction in which the force acts, i.e., $F = \dfrac{{dp}}{{dt}}$
The momentum of the body is $p = mv$ ,where $m$ is the mass of the body and $v$ is its velocity.
So Newton’ s second law can be stated as $F = ma$ , where $a$ is the body’s acceleration.