Home
Class 11
PHYSICS
A wire of length L is hanging from a fix...

A wire of length L is hanging from a fixed support. The length changes to `L_(1) and L_(2)` when masses `M_(1)and M_(2)` are suspended respectively from its free end. Then L is equal to

A

`(L_(1) + L_(2))/(2)`

B

`sqrt(L_(1)L_(2))`

C

`(L_(1) M_(2) + L_(2) M_(1))/(M_(1) + M_(2))`

D

`(L_(1) M_(2)- L_(2) M_(1))/(M_(2)- M_(1))`

Text Solution

Verified by Experts

The correct Answer is:
D
`Delta l_(1)= L_(1)- L " " F_(1)= M_(1)g`
`Delta l_(2)= L_(2)- L " " F_(2) = M_(2)g`
`Y= (F_(1)L_(1))/(A Delta l_(1))= (F_(2) L_(2))/(A Delta l_(2))`
`rArr (M_(1)g)/(L_(1)- L) = (M_(2)g)/(L_(2) - L) rArr L= (L_(1) M_(1) - L_(2) M_(1))/(M_(2)- M_(1))`
Promotional Banner

Similar Questions

Explore conceptually related problems

A wire of length L,area of cross section A is hanging from a fixed support. The length of the wire changes to L_1 when mass M is suspended from its free end. The expression for Young's modulus is:

The balancing lengths for the cells of e.m.f. E_(1) and E_(2) are l_(1) and l_(2) respectively. If they are connected separately then

The value of tension in a long thin metal wire has been changed from T_(1)" to "T_(2) . The lengths of the metal wire at two different values of tension T_(1)" and "T_(2) are l_(1) and l_(2) respectively. The actual length of the metal 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 :-

A string of length L and mass M hangs freely from a fixed point. Then the velocity of transverse waves along the string at a distance x from the free end is

Two wires of equal diameters, of resistivities rho_(1) and rho_(2) and length l_(1) and l_(2) , respectively of the combination is

Two point masses m_(1) and m_(2) are fixed to a light rod hinged at one end. The masses are at distances l_(1) and l_(2) repsectively from the hinge. Find the time period of oscillation (small amplitude) of this system in seconds if m_(1) = m_(2), l_(1) = 1m, l_(2) = 3m . If the time period is xpi , then find x .

A metal wire of length L is suspended vertically from a rigid support. When a bob of mass M is attached to the lower end of wire, the elongation of the wire is l:

When a thin iron wire of length l is heated from a temperature T_1 to T_2 , a change of 1% in its length is observed. The percentage change in area of iron plate of dimension 2l xx l when it is heated from T_1 to T_2 is