Home
Class 9
PHYSICS
A wire of length 2 m is fixed, as shown....

A wire of length 2 m is fixed, as shown. When a load is suspended from the center, it sags by 2 cm. Find the strain.

Text Solution

Verified by Experts

In right - angled triangle, `DeltaADC`
AD=1 m =100 cm = L
`DC=2` cm
`AC=L+DeltaL`
`angleD=90^(@)`
`:.` By Pythagoras theorem,
`AC^(2)+AD^(2)+DC^(2)`
`(L+DeltaL)^(2)=L^(2)|(2" cm")^(2)`
`L^(2)+2L(Delta L)+(DeltaL)^(2)=L^(2)+4" cm"^(2)`
`2L(DeltaL)=4" cm"^(2)" (neglecting "DeltaL^(2))`
`DeltaL=(4" cm"^(2))/(2L)=(4" cm"^(2))/(2xx100" cm"=0.02" cm"`
Strain `=(DeltaL)/(L)=(0.02" cm")/("100 cm")=2xx10^(-4)=0.0002`
Promotional Banner

Topper's Solved these Questions

  • ELASTICITY

    CENGAGE PHYSICS|Exercise OLYMPIAD AND NTSE LEVEL EXERCISES|10 Videos

  • ELASTICITY

    CENGAGE PHYSICS|Exercise CONSOLIDATED EXERCISE|5 Videos

  • DESCRIPTION OF MOTION

    CENGAGE PHYSICS|Exercise OLYMPIAD AND NTSE LEVEL EXERCISE|10 Videos

  • FRICTION

    CENGAGE PHYSICS|Exercise OLYMPIAD AND NTSE LEVEL EXERCISES (Read the given statements and select the correct option.)|1 Videos

Similar Questions

Explore conceptually related problems

A wire of length 2 ,m and radius 2 mm is stretched by 2.5 mm when a load of 5 kg is suspended from it Another wire of the same material put of length 1 m and radius 1 mm is attached below the load and a load of 3kg is suspended from this wire what is the total increase in length and what are the individual exensions of the wirs ?

A vertical metal cylinder of radius 2 cm and length 2 m is fixed art the lower end and a load of 10 kg is put on it. find a. the stress b. the strain and c. the compression of the cylinder. Young modulus of the metl =2xx10^11Nm^-2

Two wires W_(1) and W_(2) are made of same material and have the same length. The radius of cross-section of W_(2) is twice that of W_(1). Same load is suspended from both of them. If the strain in W_(1) is 4, then that in W_(2) will be

A metal rod of length 50cm having mass 2kg is supported on two edges placed 10cm from each end. A 3kg load is suspended at 20cm from one end. Find the reactions at the edges (take g=10m//s^(2) )

When a load of 80 N is suspended from a string, its length is 101 mm. If a load of 100 N is suspended, its length is 102 mm. If a load of 160 N is suspended form it, then the length of the string is (Assume the area of cross-section unchanged)

A mass m is suspended from a wire . Change in length of the wire is Deltal . Now the same wire is stretched to double its length and the same mass is suspended from the wire. The change in length in this case will become (it is suspended that elongation in the wire is within the proportional limit)

When a certain weight is suspended from a long uniform wire, its length increases by 1 cm. If the same weight is suspended from the other wire of the same material and length but having a diameter half of the first one then the increase in length will be

A wire loaded by a weight of density 7.8 g//c c is found to be of length 100 cm. On immersing the weight in water. The length decrease by 0.20 cm find the original length of the wire.