KVPY SX SB Exam 2013 Question Paper

Question : 96 of 120

Marks: +1, -0

A ball is rolling without slipping in a spherical shallow bowl (radius R) as shown in the figure and is executing simple harmonic motion. If the radius of the ball is doubled, the period of oscillation

increases slightly
is reduced by a factor of $1/2$
is increased by a factor of 2
decreases slightly

Validate

Solution:

\mg \sinθ- \F_\r = \ma

\F_\r=2/5mr^2a/r^2

⇒a={5/7}{g\sin θ}/{R-r}

ω=√{{5g}/{7(R-r)}}

⇒T=2π√{{7(R-r)}/{5r}}

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