Question

Newton's Laws of motion numbericals.. please explain with answer​

Answer 1

Question :

A mass M is suspended by a rope from a rigid support at A as shown in figure. Another rupe is tied at the end B, and it is pulled horizontally with a force. If the rope AB makes an angle `theta` with the vertical in equilibrium then the tension in the string AB is?

Theory :

• equilibrium of a particle

The equilibrium of a body needs both translatory as well as rotational equilibrium.

1. rotational equilibrium: in this case net external torque acting on a body is zero.i.e $\sum \: \tau \: = 0$
2. Translatory equlilbrum : when in the system to be in equilibrium

$\sum \: \vec{F} = 0$

Solution :

first draw free body diagram of Mass M.

Now resolve components of Tension .

At equlilbrum ;

Tcosθ = mg

⇒$T = \frac{mg}{ \cos( \theta) }$

and T sinθ = F

⇒$T= \frac{F }{ \sin( \theta) }$

Therefore ,

${\purple{\boxed{\large{\bold{Tension = \frac{F }{ \sin( \theta) } }}}}}$

correct option B)

$T= \frac{F }{ \sin( \theta) }$