Question

(c) A Uniform metre rule weighs 1.20 N. Weights of 0.10 N, 0.50 N, 1.0 N and 0,20 N are
suspended respectively from the 10 cm, 20 cm, 60 cm and 80 cm marks. At which mark will
the rule balance?!​

Answer 1

Explanation:

Torque due to load =4N×40cm=1.6Nm

Torque due to weight of the rule =2N×10cm=0.2Nm

Both are in opposite to each other so net torque =1.6−0.2=1.4Nm

Answer 2

The distance of mark from one end A of meter rule weigh  at which the rule  will balance is 49 cm.

Explanation:

Given:

A Uniform meter rule weighs 1.20 N.

Weights of 0.10 N, 0.50 N, 1.0 N and 0,20 N are suspended respectively from the 10 cm, 20 cm, 60 cm and 80 cm marks.

To Find:

The distance of mark from one end A of meter rule weigh  at which the rule  will balance.

Formula Used:

The torque is multiplication of  the magnitude of the force and the perpendicular distance between the point about which torque is calculated and the point of application of force.

T = F × r × sinθ

T = torque

F = linear force

r = distance measured from the axis of rotation to where the application of linear force takes place

$\theta$ = the angle between F and r

If $\theta\ is\ 90\textdegree then T=F\times r$

Solution:

Let AB is  a uniform meter rule  and  various weighs are suspended  at various marks which are measured from end A of rule.

As given, a uniform meter rule  weighs 1.20 N.

Length of uniform meter rule = 100 cm

Weighs  of role = 1.20 N and it will act at distance 50 cm from end A of scale.

As given, weights of 0.10 N, 0.50 N, 1.0 N and 0,20 N are suspended respectively from the 10 cm, 20 cm, 60 cm and 80 cm marks.

Let the distance of mark (M) from one end A of meter rule weigh  at which the rule  will balance is p.

As the meter rule is  balance.

Equating the torque by  all  weights about mark M.

$1.2(p-50)+0.1(p-10)+0.5(p-20)=1(60-p)+0.2(80-p)$

$1.2p-60+0.1p-1+0.5p-10=60-p+16-0.2p$

$1.2p+0.1p+0.5p +0.2p+p=60+16+60+1+10$

$3p=147$

$p=49 cm$

Thus,the distance of mark from one end A of meter rule weigh  at which the rule  will balance is 49 cm.

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