1800-150-456-789
FlagBACK
Flag Modern Physics> A body of mass m hangs at one end of a st...
question mark

A body of mass m hangs at one end of a string of length a the other end of which is fixed . It is given a horizontal velocity u at its lowest position so that string would just become slack when it makes angle of 60 with upward drawn verticle line find the tension in the string at point of projection

Suhail Qureshi , 6 Years ago
Grade 11
anser 1 Answers
Arun

Last Activity: 6 Years ago

At 60° angle the string becomes slack. That means that The tension in the string becomes zero and negative subsequently.  So we need to get the formula for tension in the string at an angle Ф. Let the speed of the body be v at angle Ф of the string with the vertical.
Initial KE = 1/2 m u²
Gain in PE at angle Ф : m g (1 - cos Ф)
Energy conservation:    1/2 m u² = 1/2 m v² + m g a (1 - cosФ)
=>                    v² = u² - 2 a g (1 - cosФ)      ---(1)
The forces acting on the body are the tension T along the string and the weight mg. As the body moves along a circular path, the forces are balanced along the radius.
          T = mv²/a + mg cosФ
             = m u²/a - 2 m g (1 - cosФ) + mg cosФ
         T  = m u² /a  - m g (2 - 3 cosФ)             -------  (2)
If the string becomes slack,  then T= 0 and later negative.  So at Ф = 60°,
T = 0
=>   u²/a = g (2 - 3 cos60°) = g /2 
=> u = √(ag/2)
Tension at initial point of projection Ф = 0°,  (using equation (2)
      T = m g/2 - mg (2 -3) = 3 mg/2
 

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Other Related Questions on modern physics

question mark
A particle is projected in vertical plane such that after 5 seconds its velocity becomes horizontal. The maximum height attained by the projectile from point of projection is n3 m. The value of n is _______. (g = 10 m/s2)
modern physics
1 Answer Available

Last Activity: 2 Years ago

question mark
Two particles approach each other from very large distance as shown, . if the least separation between the particles is b, what is the speed of M in center of mass frame when particles are closest? (gravity negligible)
modern physics
0 Answer Available

Last Activity: 2 Years ago

question mark
Can the sum of two equal vectors be equal to either vector
 
modern physics
0 Answer Available

Last Activity: 2 Years ago

question mark
A nucleus X184 at rest emitt alpha particle With kinetic energy 9.0MeV. The product Nucleus is Y. The values of Binding energy per nucleon of alpha particle & Y differ by 1.5MeV. The values of Binding energy per nucleon of X & Y differ by (n÷230) MeV, then n is
modern physics
0 Answer Available

Last Activity: 2 Years ago

question mark
SUBJECT: PROBLEM BASED ON LINE DETECTION.
Query: How to apply all the filters for line detection on the following piece of image (provided below)? Explain its Observations to comment on its results.
modern physics
0 Answer Available

Last Activity: 3 Years ago