Home
Class 11
PHYSICS
A boy has a catapult made of a rubber co...

A boy has a catapult made of a rubber cord of length `42 cm` and diameter `6.0 mm`. The boy stretches the cord by `20 cm` to catapult a stone of mass `20 g`. The stone flies off with a speed of `20 ms^(-1)`. Find Young's modulus for rubber. Ignore the change in the cross section of the cord in streching.

Text Solution

Verified by Experts

The potential energy stored in the cord due to stretcing is converted into the kinetc energy of the stone.
`1/2F/_\l=1/2mv^(2)implies` force `F=(mv^(2))/(/_\l)`
Strain`=(/_\l)/l`
Young's modlus `=("Stress")/("Strain")=((F/A))/(/_\l//l)=(mv^(2)//(/_\l))/(pir^(2)((/_\l)/l))`
`=2.97x10^(6)N//m^(2)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PROPERTIES OF SOLIDS AND FLUIDS

    CENGAGE PHYSICS|Exercise Exercise 5.1|12 Videos

  • PROPERTIES OF SOLIDS AND FLUIDS

    CENGAGE PHYSICS|Exercise Exercise 5.2|6 Videos

  • PROPERTIES OF SOLIDS AND FLUIDS

    CENGAGE PHYSICS|Exercise INTEGER_TYPE|2 Videos

  • NEWTON'S LAWS OF MOTION 2

    CENGAGE PHYSICS|Exercise Integer type|1 Videos

  • RIGID BODY DYNAMICS 1

    CENGAGE PHYSICS|Exercise Integer|11 Videos

Similar Questions

Explore conceptually related problems

A catapult consists of two parallel rubber strings, each of lengths 10cm and cross sectional area 10mm^2 .When stretched by 5cm, if can throw a stone of mass 100g to a vertical height of 25m. Determine Young’s modulus of elasticity of rubber.

A catapult consists of two parallel rubber strlings each of lengths, 10 cm and cross sectional area 10mm^(2) . Wen struetched by 5 cm , it can throw a stone of mass 10 gm to a vertical height of 25 m . Determine Young's modulus of elasticity of rubber.

Knowledge Check

  • A rubber cord has a cross-sectional area 10^(-6) m^(2) and total unstretched length 0.1 m. It is stretched to 0.125 m and then released to project a particle of mass 5.0 g. The velocity of projection is [Given, Young’s modulus of rubber Y = 5 xx 10^(8) N//m^(2) ]

    A
    45 m/s
    B
    30 m/s
    C
    25 m/s
    D
    15 m/s

    • Similar Questions

    Explore conceptually related problems

    A catapult consists of two parallel rubber cords each of length 20cm and cross-sectional area 5cm^(2) . When stretched by 8cm , it can throw a stone of mass 4gm to a vertical height 5m , the Young's modulus of elasticity of rubber is [g = 10m//sec^(2)]

    A rubber cord has a cross -sectional area 1 mm^(2) and total unstretched length 10.0cm . It is streched to 12.0 cm and then released to project a missile of mass 5.0 g.Taking young's modulus Y for rubber as 5.0xx10^(8) N//m^(2) .Calculate the velocity of projection .

    A mass of 100 grams is attached to the end of a rubber string 49 cm. long and having an area of cross section 20 sq. mm. The string is whirled round, horizontally at a constant speed of 40 r.p.s in a circle of radius 51 cm. Find Young's modulus of rubber.

    A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10^(-6)m^(2) stretched by an amount 0.04 m. The velocity of the projected stone is __________ m/s. (Young's modulus of rubber =0.5 xx 10^(9) N//m^(2) )

    A steel wire 4.0 m in length is stretched through 2.0 mm. The cross-sectional area of the wire is 2.0 mm^(2) . If young's modulus of steel is 2.0 xx 10^(11) Nm^(-2) , then find the energy density of wire.

    A uniform copper rod of length 50 cm and diameter 3.0 mm is kept on a frictionless horizontal surface at 20^(@)C . The coefficient of linear expansion of copper is 2.0 xx 10^(-5) K^(-1) and Young's modulus is 1.2 xx 10^(11) N//m^(2) . The copper rod is heated to 100^(@)C , then the tension developed in the copper rod is

    Consider a catapult having a 10 cm long rubber cord with a cross-sectional area of 20 mm^2 Now, if it is stretched by 4 cm to project a pebble of 10 g, then find the velocity of the pebble just after its launch (in m/s): Take Y_("rubber") = 10^8 N//m^2 .

    Home
    Profile