Question

17. A uniform metre rule of mass 100 g is balanced on a
fulcrum at mark 40 cm by suspending an unknown
mass m at the mark 20 cm.
(i) Find the value of m.
(ii) To which side the rule will tilt if the mass m is
moved to the mark 10 cm ?
(iii) What is the resultant moment now ?
(iv) How can it be balanced by another mass of
50 g ?.
>​

Answer 1

Since, uniform metre rule of mass 100 g is balanced on a fulcrum at mark 40 cm.

so, distance of c.o.m. of rule from balanced point is 10cm.

Net moment at balancing point should be zero.

So, m×20 = 100×10 m = 50g

if m is moved to mark of 10cm then rule will tilt to the side where m is suspended.

Now, for balance this

50×30 = 100×10+ 50×(x-40) (x-40) = (1500- 1000)/50 = 10cm X = 50cm.

So, another 50g mass will be suspended at 50cm mark

Answer 2

$\LARGE{ \underline{\underline{ \pink{ \bf{Required \: answer:}}}}}$

From the principle of moments,

Clockwise moment = Anticlockwise moment

100 g × (50 – 40) cm = m × (40 – 20) cm

100 g × 10 cm = m × 20 cm

m = 50 g

If the mass m is moved to the mark 10 cm, the rule will tilt on the side of mass m (anticlockwise)

Anticlockwise moment if mass m is moved to the mark 10 cm

= 50 g × (40 – 10) cm

= 50 g × 30 cm

= 1500 g cm

Clockwise moment = 100 g × (50 – 40) cm

= 100 g × 10 cm

= 1000 g cm

Resultant moment = 1500 g cm – 1000 g cm

= 500 g cm (anticlockwise)

According to the principle of moments.

Clockwise moment = Anticlockwise moment

To balance it, 50 g weight should be kept on right-hand side so as to produce a clockwise moment. Let d cm be the distance from the fulcrum. Then,

100 g × (50 – 40) cm + 50 g × d = 50 g × (40 – 10) cm

100 g × 10 cm + 50 g × d = 50 g × 30 cm

1000 g cm + 50 g × d = 1500 g cm

50 g × d = 500 g cm

Then, d = 10 cm

It can be balanced by suspending the mass 50 g at the mark 50 cm.

$\pink{}$$\red{Mark}$$\green{As}$$\blue{Brainliest}$$\orange{}$

$\pink{}$$\red{Please}$$\green{Like}$$\blue{}$$\orange{}$

${\fcolorbox{blue}{black}{\orange{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: DecentMortal\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}$