Question

4. A thread of mercury of 10.2 g is in a tube of
uniform cross-section 0.1 cmº. Calculate the
length of thread. The density of mercury is 13.6
g/cm
[Ans. 7.5 cm]​

Answer 1

Answer:

Length of thread = 7.5 cm

Explanation:

A thread of mercury of 10.2 g is in a tube of uniform cross-section 0.1 cm. And density of the mercury is 13.6 g/cm.

Here..

Mass = 10.2 g

Area of cross-section = 0.1 cm³

Density = 13.6 g/cm

Now,

Density = Mass/Volume

We have value of density and mass. But not of volume. Also l, we have to find the length.

We know that, relation between volume and length is ..

Volume = Area × Length

Substitute the known values in above formula

=> Volume = 0.1 × l

Now,

Density = Mass/Volume

Substitute the known values in above formula

=> 13.6 = 10.2/(0.1 × l)

=> l = 10.2(0.1 × 13.6)

=> l = 0.75/0.1

=> l = 7.5 cm

∴ Length of the thread is 7.5 cm.

Answer 2

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Length\:of\:thread=7.5\:cm}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about a thread of mercury whose mass is given and cross section area is given.

• We have to find the length of thread.

$\underline \bold{Given : } \\ \implies Mass\:of\:thread(M) = 10.2 \: g \\ \\ \implies Cross \: section(A) = 0.1 \: cm ^{3} \\ \\ \implies Density \: of \: mercury(D) = 13.6 \: g/cm \\ \\ \underline \bold{to \: find : }\\ \implies Length \: of \: thread(L) = ?$

• According to given question :

$\bold{By \: using \: formula : } \\ \implies Density = \frac{Mass}{Volume} - - - - - (1) \\ \\ \bold{For \: Finding \: Length} \\ \implies Volume = Cross \: section \: Area \times length \\ \\ \implies V= A\times L\\ \\ \implies V = 0.1 \times L \\ \\ \bold{Putting \: value \: of \: v\: in \: (1)} \\ \implies D = \frac{M}{0.1 \times L} \\ \\ \implies 13.6 = \frac{10.2}{0.1 \times L} \\ \\ \implies 13.6 \times 0.1 \times L= 10.2 \\ \\ \implies L = \frac{ \cancel{10.2}}{ \cancel{1.36}} \\ \\ \bold{ \implies L= 7.5 \: cm} \\ \\ \bold{\therefore Length \: of \: thread \: is \: 7.5 \: cm}$