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Question

A particle suspended from a fixed point, by a light inextensible thread of length L is projected horizontally from its lowest position with velocity 7gL2. The thread will slack after swinging through an angle θ, such that θ equal.
  1. 120o
  2. 135o
  3. 150o
  4. 30o

A
120o
B
150o
C
30o
D
135o
Solution
Verified by Toppr

As shown in figure, h=L+sinϕ
By energy conservation,
12mv2=mgh+12mv2
12×(7gl2)2=g(L+Lsinϕ)+12v2
v2=2gL2gLsinϕ+72gL
=32gL2gLsinϕ
If string slack then,
mgsinϕ=mv2L
gsinϕ=1L(v)2=1L(32gL2gLsinϕ)
gsinϕ=32g2gsinϕ
3gsinϕ=32g
sinϕ=12
ϕ=π6
θ=π2+π6=4π6=120

1024249_1045260_ans_0211b0a31f0547dfaa1f546c31bb60b7.JPG

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