# When a force $F$ acts on a body of mass $m$, the acceleration produced in the body is a. If three equal forces ${F_1},{F_2}$ and ${F_3}$ which are related as ${F_1} = {F_2} = {F_3} = F$ act on the body as shown in the figure. Then the acceleration produced is:

A. ( $\sqrt 2 - 1$ ) $a$

B. ( $\sqrt 2 + 1$ ) $a$

C. ( $\sqrt 2 $ ) $a$

D. $a$

Answer

Verified

282k+ views

**Hint:**Whenever a body is acted by some force it gets accelerated which in mathematical form it’s called Newton’s second law of motion as $F = ma$ here, we will find the net force acting on the body and its direction then will find the net acceleration of the body.

**Complete step by step answer:**

Let us find the net magnitude of forces ${F_1}$ and ${F_2}$ which are perpendicular to each other and this net force be written as ${F_{12}}$ so,

${F_{12}} = \sqrt {{F^2} + {F^2}} $

${F_{12}} = \sqrt 2 F$ Which will be in direction just opposite to that of ${F_3}$ .

Now, two forces acting on the body of mass m respectively ${F_{12}} = \sqrt 2 F$ and ${F_3} = F$.

Both forces are in opposite direction,

Hence net force act on the body of mass $m$ is,

${F_{net}} = \sqrt 2 F - F$

$\Rightarrow {F_{net}} = (\sqrt 2 - 1)F$

Now, let us assume that net acceleration is denoted by $a'$ then by newton’ second law we have:

$(\sqrt 2 - 1)F = ma'$

We also know that, $F = ma$ put this value in above equation, we get,

$(\sqrt 2 - 1)a = a'$

Net acceleration is $a' = (\sqrt 2 - 1)a$

**Hence, the correct option is A.**

**Note:**It should be remembered that, Force is a vector quantity and its added always using vector algebra which is given as ${F_{net}} = \sqrt {{F_1}^2 + {F_2}^2 + 2{F_1}{F_2}\cos \theta } $ and the direction of two equal vectors resultant is in the middle of the angle between them. And it can also be calculated with the general formula $\tan \beta = \dfrac{{{F_2}\sin \theta }}{{{F_1} + {F_2}\cos \theta }}$.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Define absolute refractive index of a medium

Which of the following would not be a valid reason class 11 biology CBSE

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What is meant by monosporic development of female class 11 biology CBSE

Trending doubts

Which of the following Chief Justice of India has acted class 10 social science CBSE

Green glands are excretory organs of A Crustaceans class 11 biology CBSE

What if photosynthesis does not occur in plants class 11 biology CBSE

What is 1 divided by 0 class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

10 slogans on organ donation class 8 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE