KVPY SX SB Exam 2015 Question Paper

Question : 24 of 120

Marks: +1, -0

Two spherical objects each of radii R and masses

m_1

and

m_2

are suspended using two strings of equal length L as shown in the figure (R << L). The angle, θ which mass

m_2

makes with the vertical is approximately -

Solution:

Using concept of COM

m_1r_1 = m_2r_2

r_1 + r_2 = 2R

(m_2/m_1+1)r_2= 2R

r^2={2m_1R}/{m_1+m_2}

L \sin θ_2 = r_2 [R < < L]

θ_2={2m_1R}/({m_1+m_2}L)

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