Question

A heavy particle hanging from a string of length l is projected horizontally with speed under root cl find speed of particle at the point where tension in the string equals weight of the particle

Answer 1

Explanation:

A heavy particle hanging from fixed point by light inextensible string of length l is projected horizontally with speed gl−−√. Find speed of particle at the instant of the motion when tension in the string is equal to weight of particle

(a)v=g3l−−√(b)v=gl3−−√(c)v=gl3(d)v=g3l

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A)

Let T=mg when angle is θ

h=l(1−cosθ)

Using concervation of energy at A and B

12m(u2−v2)=mgh

u=gl,v=speed of particle at B

v2=u2−2gh

T−mgcosθ=mv2l

mg−mgcosθ=mv2l

v2=gl(1−cosθ)-----(1)

gl(1−cosθ)=gl−2gl(1−cosθ)

cosθ=23 , Substituting in (1)

Therefore v=gl3−−√