Question

Two bodies are mass 4 kg and 5 kg are acted upon by same force. If the acceleration of lighter body is 2m/s square, the acceleration of heavier body is

Answer 1

Given :

• Masses of two bodies = 4 kg and 5 kg

• Acceleration of lighter body = 2 m/s²

To Find :

• Acceleration of heavier body when both bodies are acted upon by same force

Solution :

Among the given two bodies , lighter body is 4 kg and heavier body is 5 kg.

So , Acceleration of 4 kg body is 2 m/s².

Let the force acted upon both bodies be "F".

Relation between Acceleration , Force and mass is ,

• a = F/m

In 4 kg body case ,

• m = 4 kg
• a = 2 m/s

→ 2 m/s² = F/4 kg

→ F = 8 N

So , the force that acted upon both 4 kg and 5 kg is 8 N.

Now , Applying the force , mass and acceleration relation in 5 kg body case. Where ,

• m = 5 kg
• F = 8 N

→ a = 8 kg /5 N

→ a = 1.6 m/s²

Hence ,

• The acceleration of the heavier body i.e , 5 kg body is 1.6 m/s².

Answer 2

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${\large{\bold{\rm{\underbrace{\underline{Let's \; understand \; the \; question \; 1^{st}}}}}}}$

This question says that two bodies are mass 4 kg and 5 kg are acted upon by same force. If the acceleration of lighter body is 2m/s², what is the acceleration of heavier body ?

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${\large{\bold{\sf{\underline{Given \; that}}}}}$

$\: \: \: \:{\bullet}$ Mass of 1st body = 4 kg

$\: \: \: \:{\bullet}$ Mass of 2nd body = 5 kg

[ Both the two bodies are acted upon by same force ]

$\: \: \: \:{\bullet}$ The acceleration of lighter body = 2m/s²

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${\large{\bold{\sf{\underline{To \; find}}}}}$

$\: \: \: \:{\bullet}$ The acceleration of heavier body

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${\large{\bold{\sf{\underline{Solution}}}}}$

$\: \: \: \:{\bullet}$ The acceleration of heavier body = 1.6 m/s²

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${\large{\bold{\sf{\underline{Using \; concept}}}}}$

$\: \: \: \:{\bullet}$ Acceleration ( The relationship between acceleration , force and mass )

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${\large{\bold{\sf{\underline{Using \; formula}}}}}$

$\: \: \: \:{\bullet}$ Acceleration = ${\sf{\dfrac{F}{m}}}$

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${\large{\bold{\sf{\underline{Full \; Solution}}}}}$

~ According to the question there are 2 bodies given of different masses , 4 kg and 5 kg.

~ It is given that we have to find the acceleration of heavier body ( 5 kg ) and the acceleration of lighter body is 2m/s² ( 4 kg ).

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~ Firstly let us find the force acted on them (bodies) samely.

➨ ${\sf{A = \dfrac{F}{m}}}$

➨ ${\sf{2m/s = \dfrac{F}{4}}}$

➨ ${\sf{2m/s \times 4 = F}}$

➨ ${\sf{8 = F}}$

➨ ${\sf{F = 8N}}$

And as the question says that Two bodies are mass 4 kg and 5 kg are acted upon by same force.

Henceforth,

${\frak{8N \: is \: force \: acted \: of \: the \: bodies}}$

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~ Now let us find the acceleration of heavier body.

➨ ${\sf{A = \dfrac{F}{m}}}$

➨ ${\sf{A = \dfrac{8}{5}}}$

➨ ${\sf{A = 1.6 m/s^{2}}}$

Henceforth,

${\frak{1.6m/s^{2} \: is \: the \: acceleration \: of \: heavier \: body.}}$

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${\large{\bold{\sf{\underline{More \; knowledge}}}}}$

★ Distance = It is the length of actual path covered by a moving object in a given time interval.

★ Displacement = Shortest distance covered by a body in a definite direction is called displacement.

→ Displacement may be positive, negative or zero whereas distance is always positive.

→ Distance is a scaler quantity whereas displacement is a vector quantity both having the same unit.

→ In general magnitude of displacement ≤ Distance.

★ Speed = Distance travelled by a moving object in unit time interval is called speed i.e., speed Distance/Time. It's scaler quantity and it's SI unit is metre/second

★ Velocity = Velocity of moving object is defined as the displacement of the object in unit time interval i.e., velocity = Displacement/Time. It's vector quantity and it's SI unit is metre/second.

★ Acceleration = Acceleration of an object is defined as the rate of change of velocity of the object i.e., Acceleration = Change in velocity/Time. It's vector quantity and SI unit is m/s²

★ If Velocity decreases with time then acceleration is negative and known to be retardation.