KVPY Government Jobs Exams

Seven identical coins are rigidly arranged on a flat table in the pattern shown below so that each coin touches its
neighbors. Each coin is a thin disc of mass m and radius r. Note that the moment of inertia of an individual coin
about an axis passing through centre and perpendicular to the plane of the coin is mr2 / 2
The moment of inertia of the system of seven coins about an axis that passes through the point P (the centre of the
coin positioned directly to the right of the central coin) and perpendicular to the plane of the coins is–

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KVPY Other Question

A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let R be
the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency v about
its equilibrium shape. By dimensional analysis the ratio
3
v
σ / ρR
can be (Here σ is surface tension, ρ is density,
g is acceleration due to gravity, and k is arbitrary dimensionless constant) A loop carrying current I has the shape of a regular polygon of n sides. If R is the distance from the centre to any
vertex, then the magnitude of the magnetic induction vector B
􀁇
at the centre of the loop is