Home
Class 11
PHYSICS
A body of mass M is hanging by an inexte...

A body of mass M is hanging by an inextensible string of mass m. If the free end of the string accelerates up with constant acceleration a. find the variation of tension in the string a function of the distance measured from the mass M (bottom of the string).

Text Solution

Verified by Experts

Let T be the tension in the string at a distance x from its bottom. Referring to the FBD, we have the following equations:
Force equation for `(m_1)`:
`T=m_(1)g-Mg=(M+m_(1))a` …(i)
We are writing equation of motion for lower parts as we are not given the force acting on top of the string.
Substituting `m_(1)=(m)/(l)x` in equation (i), we have
`T=(M+(mx)/(l))(g+a)`
At `x=l, T=(M+m)(g+a)=F(say)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • NEWTON'S LAWS OF MOTION 1

    CENGAGE PHYSICS ENGLISH|Exercise Solved Examples|11 Videos

  • NEWTON'S LAWS OF MOTION 1

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 6.1|11 Videos

  • MISCELLANEOUS VOLUME 2

    CENGAGE PHYSICS ENGLISH|Exercise INTEGER_TYPE|10 Videos

  • NEWTON'S LAWS OF MOTION 2

    CENGAGE PHYSICS ENGLISH|Exercise Integer type|1 Videos

Similar Questions

Explore conceptually related problems

A mass M is hung with a light inextensible string as shown in Find the tension in the horizontal part of the string .

A small metallic sphere of mass m is suspended from the ceiling of a car accelerating on a horizontal road with constant acceleration a. The tension in the string attached with metallic sphere is

The block of mass m is at rest. Find the tension in the string A .

A block of mass m tied to a string is lowered by a distance d, at a constant acceleration of g//3 . The work done by the string is

A block of mass m tied to a string is lowered by a distance d, at a constant acceleration of g//3 . The work done by the string is

A block of mass m tied to a string is lowered by a distance d, at a constant acceleration of g//3 . The work done by the string is

A string is used to pull a block of mass m vertically up by a distance h at a constant acceleration (g)/(3) . The work done by the tension in the string is

A mass M is lowered with the help of a string by a distance h at a distance acceleration g//2 . The work done by the string will be

A bob of mass 1 kg is suspended from an inextensible string of length 1 m. When the string makes an angle 60^(@) with vertical, speed of the bob is 4 m/s Net acceleration of the bob at this instant is

A bob of mass m hangs from the ceiling of a smooth trolley car which is moving with a constant acceleration a. If young's modulus, radius and length of the string are Y, r and I , respectively, find the (a) stress in the string and (b) extension of the string when it makes a constant angle relative to vertical.

Home
Profile