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Classical Mechanics Level 4

A block of mass \(2 \ \text{kg}\) slides down an inclined plane of inclination \(30^{\circ}\). The coefficient of friction between the block and plane is \(0.5\). The magnitude of contact force between block and plane can be expressed in the form \(\sqrt{a} \ \text{N}\) where \(a\) is a positive nonsquare integer.

Find the sum of digits in \(a\).

Assume the plane is fixed. Take \(g = 10 \ \text{ms}^{-2}\).

This Question Is Inspired From An Old JEE Question


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