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**6. Body is in equilibrium : -**

We can say rigid body is in equillibrium when it is in

(a) Translational equilibrium

F_{net x} = 0 and F_{net y} = 0 and

(b) Rotational equilibrium

**Note :**

(i) If net force on the body is zero then net torque of the forces may or may not be zero.

**example. **

A pair of forces each of same magnitude and acting in opposite direction on the rod.

**(2) **If net force on the body is zero then torque of the forces about each and every point is same

t about B

t about C

**Ex.18** *Determine the point of application of third force for which body is in equillibrium when forces of 20 N & 30 N are acting on the rod as shown in figure *

** **

**Sol. **Let the magnitude of third force is F, is applied in upward direction then the body is in the equilibrium when

(i) (Translational Equillibrium)

⇒ 20 + F = 30 ⇒ F = 10 N

So the body is in translational equilibrium when 10 N force act on it in upward direction.

(ii)

Let us assume that this 10 N force act. Then keep the body in rotational equilibrium So Tor que about C = 0

30 x 20 = 10 x

x = 60 cm

so 10 N force is applied at 70 cm from point A to keep the body in equilibrium.

**Ex.19 Determine the point of application of force, when forces are acting on the rod as shown in figure.**

**Sol. **Since the body is in equillibrium so we conclude and torque about any point is zero i.e.,

Let us assume that we apply F force downward at A angle q from the horizontal, at x distance from B

⇒ F_{net} x = 0 which gives

F_{2} = 8 N

From F_{net y} = 0 ⇒ 5 + 6 = F_{1 }+ 3

⇒ F_{1} = 8 N

If body is in equilibrium then torque about point B is zero,

⇒ 3 x 5 + F_{1} x - 5 x 10 = 0

⇒ 15 + 8x - 50 = 0

**Ex.20 A uniform rod length l, mass m is hung from two strings of equal length from a ceiling as shown in figure. Determine the tensions in the strings ? **

** **

**Sol. **Let us assume that tension in left and right string is T_{A} and T_{B} respectively. Then

Rod is in equilibrium then

From

mg = T_{A} + T_{B} ...(1)

*Ladder Problems :*

**Ex.21 A stationary uniform rod of mass `m', length `l' leans against a smooth vertical wall making an angle q with rough horizontal floor. Find the normal force & frictional force that is exerted by the floor on the rod? **

** **

**Sol. **As the rod is stationary so the linear acceleration and angular acceleration of rod is zero.

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