Home
Class 11
PHYSICS
A uniform rod of length L and mass M is ...

A uniform rod of length `L` and mass `M` is pulled horizontally on a smooth surface with a force `F`. Determine the elongation of rod if Young's modulus of the material is `Y`.

Text Solution

Verified by Experts

Under the action of the external force, the rod accelerates with `a=F//m`. The magnitude of stress decreases as one moves away from the point of application of the force. Therefore, the strain also decreases as one moves towards the free end.

Determine the total elongation of the rod, let us consider a small element of length `dx` at a distance `x` from the free end of the rod. The magnitude of force at this section is `F'=Fx//L`.
Therefore, the stress at this section is
`sigma=(F')/A=F/A x/L`
and elongation `ddelta` produced in this differential element is
`ddelta=F/(YAL)xdx`
Thus, total elongation is
`delta=F/(YAL)int_(0)^(1)x dx=F/(YAL)[(x^(2))/2]_(0)^(1)`
or`delta=1/2(FL)/(YA)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF SOLIDS AND FLUIDS

    CENGAGE PHYSICS|Exercise Solved Examples|11 Videos

  • PROPERTIES OF SOLIDS AND FLUIDS

    CENGAGE PHYSICS|Exercise Exercise 5.1|12 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 uniform rod of length (L) and area of cross-section (A) is subjected to tensil load (F). If sigma be the Poisson's ratio and Y be the Young's modulus of the material of the rod, then find the volumetric strain produced in the rod.

A uniform rod of length L and mass M has been placed on a rough horizontal surface. The horizontal force F applied on the rod is such that the rod is just in the state of rest. If the coefficient of friction varies according to the relation mu =Kx where K is a +ve constant. Then the tension at mid point of rod is?

A uniform rod of length L and density rho is being pulled along a smooth floor with a horizontal acceleration alpha (see Fig.) The magnitude of the stress at the transverse cross-section through the mid-point of the rod is……..

A 5 kg rod of square cross section 5 cm on a side and 1m long is pulled along a smooth horizontal surface by a force applied at one end. The rod has a constant acceleration of 2 ms^(-12) . Determine the elongation in the rod. (Young's modulus of the material of the rod is 5 xx 10^(3) N//m^(9) ).

One fourth length of a uniform rod of length 2l and mass m is place don a horizontal table and the rod is held horizontal. The rod is released from rest. Find the normal reaction on the rod as soon as the rod is released.

A rod of length L kept on a smooth horizontal surface is pulled along its length by a force F. The area of cross-section is A and Young's modulus is Y. The extension in the rod is

A uniform rod of mass M and length L, area of cross section A is placed on a smooth horizontal surface. Forces acting on the rod are shown in the digram Ratio of elongation in section PQ of rod and section QR of rod is

A uniform rod of mass M and length L lies flat on a frictionless horizantal surface. Two forces F and 2F are applied along the length of the rod as shown. The tension in the rod at point P is

A uniform rope of length of length L is pulled by a force F on a smooth surface. Find tension in the rope at a distance x from the end where force is applied.