Home
Class 11
PHYSICS
A sphere of mass m attached with the fre...

A sphere of mass `m` attached with the free end of a steel wire of length `l` swings in the veritical plane form the horizontal positon.

Elongation of the wire in the vericle positon is

A

`(mgl)/(Y(pi r^(2)))`

B

`(2mgl)/(Y(pi r^(2)))`

C

`(mgl)/(3Y(pi r^(2)))`

D

`(3mgl)/(Y(pi r^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
D
`Delta l = ((F_("net")l))/(YA) , V = sqrt(2gl)`
`= ((mg + (mv^(2))/(l))l)/(YA) = ((mg + 2mg)l)/(YA)`
`Deltas L = (3mgl)/(Y(pi r^(2))), v = (1)/(2)Fe, U = (YA)/(2l) xx (Delta l)^(2) = (9m^(2) g^(2) l)/(2Y pi r^(2))`
Promotional Banner

Topper's Solved these Questions

  • MECHANICAL PROPERTIES OF SOLIDS

    NARAYNA|Exercise Comprehension-2:|2 Videos

  • MECHANICAL PROPERTIES OF SOLIDS

    NARAYNA|Exercise Comprehension-3:|2 Videos

  • MECHANICAL PROPERTIES OF SOLIDS

    NARAYNA|Exercise SINGLE ANSWER TYPE QUESTIONS|13 Videos

  • MECHANICAL PROPERTIES OF FLUIDS

    NARAYNA|Exercise EXERCISE - III|30 Videos

  • MOTION IN A PLANE

    NARAYNA|Exercise Level-II(H.W)|31 Videos

Similar Questions

Explore conceptually related problems

A sphere of mass m attached with the free end of a steel wire of length l swings in the veritcle plane form the horizontal positon. Elastic energy should in the wire in the vericle positon is

A sphere of radius 10 cm and mass 25 kg is attached to the lower end of a steel wire of length 5 m and diameter 4 mm which is suspended from the ceiling of a room . The point of support is 521 cm above the floor. When the sphere is set swinging as a simple pendulum, its lowest point just grazes the floor. Calculate the velocity of the ball at its lowest position (Y_(steel) = 2xx10^(11) N//m^(2)) .

A body of mass M is attached to the lower end of a metal wire, whose upper end is fixed . The elongation of the wire is l .

A wire of length 1m fixed at one end has a sphere attached to it at the other end. The sphere is projected hroizonatally with a veloicity of sqrt(9g) . When it decribes a vertical circle the ratio of elongations of the wire when the sphere is at top and bottom of the circle is

A sphere of radius 0.1m and mass 8 pi kg is attached to the lower end of a steel wire of length 5.0 m and diameter 10^(-3) . The wire is suspended from 5.22 m high ceiling of a room . When the sphere is made to swing as a simple pendulum, it just grazes the floor at its lowest point. Calculate the velocity of the sphere at the lowest position . Young's modulus of steel is (1.994xx10^(11) N//m^(2)) .

A copper wire of negligible mass, length l and corss-section A is kept on a smooth horizontal tabel with one end fiexed. A ball of mass m is attached to the other end. The wire and the ball are rotating with an angular velocity omega . If elongation in the wire is Deltal , obtain the expression for the Young's modulus.

A body of mass M is attached to lower end of a metal wire whose upper and is fixed. The elongation is l. The ratio of loss of gravitational potential energy to the energy stored in the wire is

A stone of mass m tied to one end of a wire of length L. the diameter of the wire is D and it is suspended vertically. The stone is now rotated in a horizontal plane and makes an angle 6 with the vertical. If Young's modulus of the wire is Y , Then the increase in the length of the wire is

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:

Knowledge Check

  • A sphere of mass m attached with the free end of a steel wire of length l swings in the veritcle plane form the horizontal positon. Elastic energy should in the wire in the vericle positon is

    A
    `(9m^(2) g^(2)l)/(2Ypi r^(2))`
    B
    `(7m^(2) g^(2)l)/(2Ypi r^(2))`
    C
    `(9m^(2) g^(2)l)/(Ypi r^(2))`
    D
    `(9m^(2) g^(2)l)/(4Ypi r^(2))`

  • A body of mass M is attached to the lower end of a metal wire, whose upper end is fixed . The elongation of the wire is l .

    A
    Loss in gravitational potential energy of` M` is `Mgl`
    B
    The elastic potential energy stored in the wire is ` Mgl`
    C
    The elastic potential energy stored in the wire is `1/2 Mgl`
    D
    Heat produced is `1/2 Mgl`

  • A wire of length 1m fixed at one end has a sphere attached to it at the other end. The sphere is projected hroizonatally with a veloicity of sqrt(9g) . When it decribes a vertical circle the ratio of elongations of the wire when the sphere is at top and bottom of the circle is

    A
    `2:5`
    B
    `5:2`
    C
    `3:5`
    D
    `5:3`