Question

A force acting on a body of mass m gives acceleration 2m /s2. If 2kg mass is added to m and the same force gives an acceleration 1m/s2. The value of m is
1kg, 2kg, 3kg, 4kg​

Answer 1

$\large \rm {\underbrace{\underline{Elucidation:-}}}$

$\sf \blue {\maltese{\underline{\underline{Provided\: that:-}}}}$

$\sf {Mass\: of\: body=m}$

$\sf {Acceleration (a)=2m/s^{2}}$

$\sf \pink {\maltese{\underline{\underline{It's \: known\: that:-}}}}$

➻By the definition of force it can be formulated as,

$\cal \implies \green {\fbox{F=m×a}}$

$\sf \mapsto {F=m×2m/s^{2}}$

$\sf \mapsto {F=2m}$⟶①

$\sf \orange {\maltese{\underline{\underline{Now:-}}}}$

➻If 2kg mass is added to m.

$\sf {Mass\: of\: body=m+2}$

$\sf {Acceleration (a)=1m/s^{2}}$

$\sf \purple {\maltese{\underline{\underline{Applying\: the \: same\: formula:-}}}}$

$\sf \mapsto {F=m+2×1m/s^{2}}$

$\sf \mapsto {F=m+2}$⟶②

➻Since the same force is acting in both the conditions we can equate both the equations.

$\sf \mapsto {2m=m+2}$

$\sf \mapsto {2m-m=2}$

$\large \cal \implies \green {\fbox{m=2}}$

$\sf \red {\maltese{\underline{\underline{Thenceforth,}}}}$

➻The value of 'm' is "2kg" respectively.

Answer 2

Given: A force acting on a body of mass m gives acceleration 2 ms⁻². 2kg mass is added to m and the same force gives an acceleration 1 ms⁻².

To find: The value of m.

Solution:

• Force is an external cause that changes or tends to change the state of motion or of rest of exhibited by the body.
• Acceleration of a body is the change in its velocity with respect to time.
• They are related as,

        $F = m * a$

• Here, F is the force and m is the mass and a is the acceleration produced.
• So, when the force gives an acceleration 2 ms⁻²,

       $F = m * 2 ms^{-2}$

• When the 2 kg mass is added and the acceleration given is 1 ms⁻²,

       $F = (m+2kg) * 1ms^{-1}$

• The force is same in both the cases and hence, they can be equated.

        $m * 2ms^{-1} = (m+2kg) * 1ms^{-1}$

        $m = 2 kg$

Therefore, the value of m is 2 kg.