Exams › JEE Main › Physics

An insect crawls very slowly up a hemispherical surface (see figure). The coefficient of friction between the surface and the insect is 1/3. If the line joining the centre of the hemisphere to the insect makes angle alpha with the vertical, the maximum possible value of alpha satisfies:

1. cot alpha = 3
2. tan alpha = 3
3. sec alpha = 3
4. cosec alpha = 3

Correct answer: cot alpha = 3

Solution

At the maximum angle, the component of gravity down the slope equals the limiting friction: mg sin alpha = mu mg cos alpha, so tan alpha = mu = 1/3, i.e. cot alpha = 3.

Related JEE Main Physics questions

• Which of the following has the same SI unit as impulse?
• A monkey slides downward from a tree branch with uniform acceleration. If the maximum tension the branch can withstand is 75% of the monkey’s weight, what is the least downward acceleration that will allow the monkey to descend without snapping the branch?
• A 1000 kg car is travelling at 30 m/s. The brakes are applied until it stops. If the friction force between the tyres and the road is 5000 N, how long will the car take to come to rest?
• A rocket initially ejects gas from its rear at a mass rate of 0.1 kg s⁻¹. If the exhaust speed relative to the rocket is 50 m s⁻¹ and the rocket’s mass is 2 kg, what is its acceleration in m s⁻²?
• A block of mass M rests on a rough level floor with coefficient of friction μ. A person applies a horizontal pull, but the block remains at rest. If the total contact force exerted by the floor on the block is F, then
• Which of the following types of motion on a frictionless plane surface occurs without any force acting on the body?

⚔️ Practice JEE Main Physics free + battle 1v1 →