Home
Class 11
PHYSICS
At 40^(@)C a brass wire of 1mm radius is...

At `40^(@)C` a brass wire of 1mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from` 40^(@)C` to `20^(@)C` it regains its original length of 0.2 m the value of M is close to (coefficient of linear expansion and young's modulus of brass are `10^(-5)//.^(@)C` and `10^(11)//N//m^(2)` respectively `g=10ms^(-2))`

A

6.28 Kg

B

1.5 Kg

C

0.9 Kg

D

0.5 Kg

Text Solution

Verified by Experts

The correct Answer is:
A
`(Mgl)/(A Delta l)=Y`
`therefore Delta l_("mechanical")=(Mg l)/(AY)`
`Delta l_("thermal")=l alpha Delta T = l alpha xx 20`
`(Mgl)/(AY)=20 alpha l`
`M=(20xx10^(-5)xx pi xx 1 xx 10^(-6)xx10^(11))/(10)=6.28` Kg
Promotional Banner

Similar Questions

Explore conceptually related problems

Steel wire of length 'L' at 40^@C is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from 40^@C to 30^@C to regain its original length 'L'. The coefficient of linear thermal expansion of the steel is 10^-5//^@C , Young's modulus of steel is 10^11 N//m^2 and radius of the wire is 1mm. Assume that L gt gt diametere of the wire. Then the value of 'm' in kg is nearly

A steel wire 2 m long is suspended from the ceiling. When a mass is hung from its lower end, the increase in length recorded is 1 cm . Determine the strain in the wire.

A steel scale is correct at 0^(@)C . The length of a brass tube measured by it at 40^(@)C is 4.5m . The correct length of the tube at 0^(@)C is (Coefficients of linear expansion of steel and brass are 11 xx 10^(-6//@)C and 19 xx 10^(-6//@)C respectively).

A steel wire of length 20 cm and uniform cross-section 1mm^(2) is tied rigidly at both the ends. If the temperature of the wire is altered from 40^(@)C to 20^(@)C , the change in tension. [Given coefficient of linear expansion of steel is 1.1xx10^(5) .^(@)C^(-1) and Young's modulus for steel is 2.0xx10^(11) Nm^(-2) ]

A brass wire 2 m long at 27^@C is held taut with negligible tension between two rigid supports. If the wire is cooled to a temperature of -33^@C , then the tension developed in the wire, its diameter being 2 mm, will be (coefficient of linear expansion of brass =2.0xx10^(-5)//^(@)C and Young's modulus of brass =0.91xx10^(11)Pa )

A wire of cross-sectional area 3 mm^(2) is first stretched between two fixed points at a temperature of 20^(@)C . Determine the tension when the temperature falls to 10^(@)C Coefficient of linear expansion alpha=10^(-5).^(@)C^(-1) and Y =2 xx10^(11) N//m^(2)

A copper wire of length l and radius 2 mm is suspended from a fixed support vertically and a mass m is hung from its other end. The wire initially at 30^@C is cooled down to 20^@C to bring it back to its original length l . The coefficient of linear thermal expansion of the copper is 1.7 xx 10^(-5) "'^@C^(-1) . If l >> the diameter of wire,then find the value of m/5 in kg close to nearest integer. Take, g = 10 m//s^2 , Y = 1.1 xx 10^11 N//m^2

How much force is required to produce an increase of 0.2 % in the length of a brass wire of diameter 0.6 mm (Young's modulus for brass =0.9 xx 10^(11) N//m^(2) )