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Question

The length of a conical pendulum is l=2 m and its bob has a mass of m=0.2 kg. The string will break if the tension T exceeds 4 N and g=10 m/s2. Then the smallest angle the string can make with the horizontal is

A
60
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B
30
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C
15
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D
45
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Solution

The correct option is B 30
The diagram of the system is given below.


From FBD of the bob:

Tcosθ=mg ... (1)
and Tsinθ=mv2r ... (2)
(Tsinθ provides necessary centripetal force)

From (1) & (2), tanθ=v2rg ... (3)

Given that Tmax=4 N; mass of bob =0.2 kg
From equation (1) and (2) we get
(Tcosθ)2+(Tsinθ)2=(mv2r)2+(mg)2
T2=(mv2r)2+(mg)2
To find v for Tmax:
mv2r=T2max(mg)2
v2r=1mT2max(mg)2
v2r=10.242(0.2×10)2
=54222
=103
From equation (3)
tanθ=10310
tanθ=3
θ=60
So, the angle from the horizontal will be 300

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