Question

A force acts on an object of 4kg to produce an
acceleration of 3 m/s2. If the same force acts
on an object of 6 kg, the acceleration produced
is_m/s2​

Answer 1

Answer :

›»› The acceleration produced by the object is 2 m/s².

Given :

• A force acts on an object of 4kg to produce an acceleration of 3 m/s².
• The same force acts on an object of 6 kg.

To Calculate :

• The acceleration produced by the object.

Calculation :

Here in this question we have to calculate the acceleration produced by the object when the same force acts on an object of 6 kg. So, firstly we need to find the force acts on the object, after that we will calculate the acceleration produced by the object on the basis of conditions given above.

We can find the force acts on the object by using the second law of Newton which says F = ma.

And, we can also calculate the acceleration produced by the object by using the second law of Newton which says F = ma.

Finding force acts on the object.

From second law of Newton.

→ F = ma

→ F = 4 × 3

→ F = 12 N

Now,

Calculating acceleration produced by the object.

From second law of Newton.

→ F = ma

→ 12 = 6 × a

→ 12 = 6a

→ a = 12/6

→ a = 2

Hence, the acceleration produced by the object is 2 m/s².

Verification :

→ F = ma

→ 12 = 6 × 2

→ 12 = 12

Here, LHS = RHS

Hence Verified !

Answer 2

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question :- \: \star}}}}}$

A force acts on an object of 4kg to produce an acceleration of 3 m/s2. If the same force acts on an object of 6 kg, the acceleration produced is_m/ss2.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

$\huge{\sf{A = 2 \: metre \: per \:second}}$

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

Mass of 1st object = 4kg

Acceleration of 1st object = 3m/s²

Mass of second object = 6kg

Force of object 1 = force of object 2

Now ,

$\Large{\underline{\underline{\bf{Find :-}}}}$

acceleration produced

is_m/ss2?

$\Large{\underline{\underline{\bf{Solution:-}}}}$

First we need to find out force.

So, what's the force basically

• A push or pull acting on a body which tends to change its state of rest or of is defined as Force.

• A force has both magnitude and direction making it a vector quantity.

• A force is equal to the product of body Mass and Acceleration.

$\underline{\boxed{\textsf{F = {\textbf{ma}}}}} \qquad\qquad \bigg\lgroup\bold{Formula \ for \ Force} \bigg\rgroup$

Here,

Mass of the body = " m "

Acceleration = " a"

Force = " F "

Now,

As per the question :-

✦ F = ma

✦ F = 4 × 3

✦ Force = 12 N

Therefore ,

Applying same law of motion again :-

In order to find Acceleration :-

✦ F = ma

✦ 12 = 6 × a

✦ 12 = 6a

✦ a = 12/6

✦ Acceleration = 2m/s²

$\\ \huge{\leadsto \ \underline{\boxed{\sf{Acceleration = 2metre per sec.}}}}$

More to know :-

We can even derive the relation F = ma from Newton's law of motion.

$\large{\boxed{\bold{Newton's\:Second\:Law}}}$

The rate of change of momentum of an object depends upon the direction and magnitude of applied force.

$\large{\sf{F \propto \frac{dp}{dt}}}$

$\large{\leadsto \ \sf{F \propto \frac{d(mv - mu)}{dt}}}$

$\large{\leadsto \ \sf{F = k.m \frac{d(v - u)}{dt}}}$

$\large{\leadsto \ \sf{F = k.ma}} \\ \\ \sf{[If, k = 1]}$

$\\ \huge{\leadsto \ \underline{\boxed{\sf{F = ma}}}}$

☆What is the SI unit of Force?

$\red{\bigstar}$ S. I unit of Force

$\huge\leadsto{\sf\purple{Newton\: N}}$

◆ C.G.S (centimetre gram second) unit of force is dyne.

☆ Define direction of force?

◆ The direction in Which the body is pushed or pulled is called direction of the force.

☆ What are the Basic effects of force?

$\sf\underline{\purple{\:\:\: \: \: Effects\: of\: the \: Force \:\:\:}}$

❀ A force can change the direction of a moving object.

❀ A force can change the shape and size of an

object.

❀ A force can change the speed of a moving object.

❀ A force acting on a body can change its state of motion or rest.

✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:**✧･ﾟ:*