You visited us 1 times! Enjoying our articles? Unlock Full Access!

Thermal Expansion

The length of...

Question

The length of wire, when $M_{1}$ is hung from it is $l_{1}$ and is $l_{2}$ with both $M_{1}$ and $M_{2}$ hanging. The natural length of wire is

\frac{M_{1}}{M_{2}} (l_{1} - l_{2}) + l_{1}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{M_{2} l_{1} - M_{1} l_{2}}{M_{1} + M_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{l_{1} + L_{2}}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{l_{1} L_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{M_{1}}{M_{2}} (l_{1} - l_{2}) + l_{1}$
Let the natural length of wire be $l$ .

When only $M_{1}$ is hanging, the external force acting on the wire is

$F = M_{1} g$

Now using Hooke's law,

$Δ L = \frac{F L}{A Y}$

$\Rightarrow (l_{1} - l) = \frac{(M_{1} g) l}{A Y} . . . . . . . . . (1)$

Here, $Y =$ Young's modulus
$A =$ cross-sectional area of wire

When both $M_{1}$ and $M_{2}$ are hanging, external force will be

$F_{e x t} = (M_{1} + M_{2}) g$

Again using formula of elastic constant

$Δ l = \frac{F_{e x t} L}{A Y}$

$\Rightarrow (l_{2} - l) = \frac{(M_{1} + M_{2}) g l}{A Y} . . . . . (2)$

Here, $l_{1}$ and $l_{2}$ are length of wire when $M_{1}$ and $(M_{1} + M_{2})$ are hanging.

From Eqs. $(1) & (2)$ ,

$\frac{l_{2} - l}{l_{1} - l} = \frac{M_{1} + M_{2}}{M_{1}}$

$\Rightarrow M_{1} l_{2} - M_{1} l = l_{1} (M_{1} + M_{2}) - l (M_{1} + M_{2})$

$\Rightarrow l = \frac{M_{1}}{M_{2}} (l_{1} - l_{2}) + l_{1}$

So, option $(a)$ is correct.

Suggest Corrections

Similar questions

Q. The length of wire when

M_{1}

is hung from it is

l_{1}

and is

l_{2}

with both

M_{1}

and

M_{2}

hanging. The natural length of wire is

Q. A wire of length

L

with Young's modulus

Y

is hanging from a fixed support. The length of wire becomes

L_{1}

when mass

M_{1}

is suspended, and it becomes

L_{2}

when mass

M_{2}

is suspended at its free end. Then, the original length

L

is equal to -

Q. If two simple pendulums first of bob mass

M_{1}

and length

l_{1}

, second of bob mass

M_{2}

and length

l_{2}

. Given

M_{1} = M_{2}

and

l_{1} = 2 l_{2}

. If the vibrational energies of both are same, then which of the following is correct?

Q. The length of a wire is

l_{1}

when tension is

T_{1}

and

l_{2}

when tension is

T_{2}

. The natural length of the wire is

Q. When the tension in a metal wire is

T_{1}

, its length is

l_{1}

. When the tension is

T_{2}

, its length is

l_{2}

. The natural length of wire is

Join BYJU'S Learning Program

Explore more

Thermal Expansion

Standard XII Physics

Join BYJU'S Learning Program

The length of wire, when M1 is hung from it is l1 and is l2 with both M1 and M2 hanging. The natural length of wire is

The length of wire, when $M_{1}$ is hung from it is $l_{1}$ and is $l_{2}$ with both $M_{1}$ and $M_{2}$ hanging. The natural length of wire is