KVPY SX SB Exam 2015 Question Paper

Question : 95 of 120

Marks: +1, -0

Two small metal balls of different mass m

_1

and m

_2

are connected by strings of equal length to a fixed point. When the balls are given equal charges, the angles that the two strings make with the vertical are 30º and 60º, respectively. The ratio

m_1/m_2

is close to -

1.7
3.0
0.58
2.0

Validate

Solution:

θ_1 = 30º, θ_2 = 60º

using Lami theorem on m

_1

F/{\sin(π-θ_1)}={m_1g}/{\sin(π-α)}

F/{\sin(π-θ_1)}={m_1g}/{\sin α }

...(1)
using Lami theorem on m

_2

F/{\sin(π-θ_2)}={m_2g}/{\sin(π-α)}

F/{\sin θ_2 }={m_2g}/{\sin α }

...(2)
using (1) & (2)

m_1 \sin θ_1 = m_2 \sin θ_2

m_1 × \sin 30º = m_2 \sin 60º

m_1/m_2=√3=1.7

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