There are four forces acting at a point P produced by strings as shown in figure. Which is at rest ?

English

Gujarati

Hindi

4-1.Newton's Laws of Motion

medium

There are four forces acting at a point $P$ produced by strings as shown in figure. Which is at rest ? Find the forces $F_1$ and $F_2$.

Option A

Option B

Option C

Option D

Solution

Let $\mathrm{F}_{3}=1 \mathrm{~N}$ (given)

$\mathrm{F}_{4}=2 \mathrm{~N}$ (given)

String is at rest,

$\Sigma \overrightarrow{\mathrm{F}}=0$

$\Sigma \mathrm{F}_{x}=0$

$\mathrm{~F}_{2}+1 \cos 45-2 \cos 45=0$

$\mathrm{~F}_{2}+\cos 45(1-2)=0$

$\mathrm{~F}_{2}+\frac{1}{\sqrt{2}}(-1)=0$

$\mathrm{~F}_{2}=\frac{1}{\sqrt{2}} \mathrm{~N}$

$\Sigma \mathrm{F}_{y}=0$

$1 \sin 45+2 \sin 45-\mathrm{F}_{2}=0$

$3 \sin 45-\mathrm{F}_{2}=0$

$\mathrm{~F}_{2}=3 \sin 45$

$=\frac{3}{\sqrt{2}}$

$=2.121 \mathrm{~N}$

Standard 11

Physics

Share

Similar Questions

A particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously (Assuming particle is initially at rest)
${\vec F_1} = 5\hat i – 5\hat j + 5\hat k$ ${\vec F_2} = 2\hat i + 8\hat j + 6\hat k$
${\vec F_3} = – 6\hat i + 4\hat j – 7\hat k$ ${\vec F_4} = – \hat i – 3\hat j – 2\hat k$
Then the particle will move

medium

A weight can be hung in any of following four ways by using same string. In which case is the string more likely to break is :-

medium

A body of mass $m_1$ exerts a force on another body of mass $m_2$. If the magnitude of acceleration of $m_2$ is $a_2$, then the magnitude of the acceleration of $m_1$ is (considering only two bodies in space)

easy

A smooth cylinder of mass $m$ and radius $R$ is resting on two corner edges $A$ and $B$ as shown in fig. The relation between normal reaction at the edges $A$ and $B$ is

medium

A false balance has equal arms. An object weigh $X$ when placed in one pan and $Y$ when placed in other pan, then the weight $W$ of the object is equal to

easy