Home
Class 11
PHYSICS
A sphere of mass 3 kg is attached to one...

A sphere of mass 3 kg is attached to one end of a steel wire of length 1 m and radius 1mm. It is whirled in a vertical circle with an angular velocity of 2 rev `//` s. What is the elongation of the wire, when the weight is at the lowest point of its path? Y for steel `= 20 xx 10^(10) N //m^(2)`.

Text Solution

Verified by Experts

`m = 3 kg`
Length of the wire `= L = 1m `
Radiu `= r = 1.0 xx 10^(-3) m`
Frequency `= n = 2` rev `//` s
Elongation = l = ?
Young.s modululs `= Y = 20 xx 10^(10) N //m^(2)`
`Y = ( F)/( A)xx( L )/(l ) = ( TL )/( Al)`
`l = ( TL )/( YA)`
where T is the tensionin the wire when the sphere is at the bottom
`T = m R omega^(2) + mg`
The length of the wire is the radius, `i.e. L = R = 1m`
`omega = 2 pi n = 4pi ` rad` //` s
`T = 3 xx 1 xx ( 4pi )^(2) + 3 xx 9.8`
`= 502.66N`
Area of cross -section of the wire `=A = pi r^(2) = 3.14 xx ( 10^(-3))^(2)`
`l = ( TL)/(YA ) = ( 502.66 xx 1)/( 20 xx 10^(10) xx 3.14 xx (10^(-3))^(2))`
`= 8.004 xx 10^(-4) m`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF MATTER

    ICSE|Exercise MODULE 2 (SOLVED EXAMPLES)|22 Videos

  • PROPERTIES OF MATTER

    ICSE|Exercise MODULE 3 (SOLVED EXAMPLES)|31 Videos

  • OSCILLATIONS

    ICSE|Exercise SELECTED PROBLEMS (OSCILLATION IN A TUNNEL BORED THROUGH THE EARTH)|2 Videos

  • SAMPLE QUESTION PAPER - 01

    ICSE|Exercise SECTION - D|12 Videos

Similar Questions

Explore conceptually related problems

One end of a string of length 1 m is tied to a body of mass 0.5 kg. It is whirled in a vertical circle with angular velocity 4 rad s^(-1) . Find the tension in the string when the body is at the lower most point of its motion. (take, g = 10 ms^(-1) )

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1m, is whirled in a vertical circle with an angular velocity of 2 rev.//s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm^(2) . Calculate the elongation of the wire when the mass is at the lowest point of its path Y_(steel) = 2 xx 10^(11) Nm^(-2) .

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1m, is whirled in a vertical circle with an angular velocity of 2 rev.//s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm^(2) . Calculate the elongaton of the wire when the mass is at the lowest point of its path Y_(steel) = 2 xx 10^(11) Nm^(-2) .

A steel wire of 1.5 m long and of radius 1 mm is attached with a load 3 kg at one end the other end of the wire is fixed it is whirled in a vertical circle with a frequency 2 Hz. Find the elongation of the wire when the weight is at the lowest position Y=2xx10^(11)N//m^(2) and (g=10m//s^(2))

A 6 kg weight is fastened to the end of a steel wire of un stretched length 60 cm . It is whirled in a vertical circle and has an angular velocity of 2 rev//s at the bottom of the circle. The area of cross - section of the wire is 0.05 cm ^(2) . Calculate the elongation of the wire when the weight is at the lowest point of the path . Young's modulus of steel = 2xx10 ^(11) N //m^(2) .

A copper wire of negligible mass, 1 m length and cross-sectional area 10^(-6) m^(2) is kept on a smooth horizontal table with one end fixed. A ball of mass 1 kg is attached to the other end. The wire and the ball are rotating with an angular velocity of 20 rad//s . If the elongation in the wire is 10^(-3) m . a. Find the Young's modulus of the wire (in terms of xx 10^(11) N//m^(2) ). b. If for the same wire as stated above, the angular velocity is increased to 100 rad//s and the wire breaks down, find the breaking stress (in terms of xx 10^(10) N//m^(2) ).

A 1kg stone at the end of 1m long string is whirled in a vertical circle at a constant speed of 4m//s . The tension in the string is 6N , when the stone is at (g=10m//s^(2))

A stone of mass 1kg is tied with a string and it is whirled in a vertical circle of radius 1 m. If tension at the highest point is 14 N, then velocity at lowest point will be

A block of weight 10 N is fastened to one end of a wire of cross sectional area 3 mm^2 and is rotated in a vertical circle of radius 20 cm. The speed of the block at the bottom of the circle is 2ms^-1 . Find the elongation of the wire when the block is at the bottom of the circle. Young modulus of the material of the wire =2xx10^11Nm^-2 .

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)) .