# Mechanics-I past question paper

Q1: Two inclined planes have a common vertex and a string passing over a small pulley at the vertex supports two equal weights. If one of the planes be rough and the other is smooth. Find relation between inclinations of planes when weight on smooth plane and is on point of moving?(10)

Q2: Explain the resolution of a system of coplanar and parallel forces?(10)

Q3: Prove that any system of forces in a plane is equivalent to three suitably chosen forces X, Y, Z acting along the sides BC, CA, AB of a given A in the plane. Prove that if the system is equivalent to a couple G, then

X/BC= Y/CA = Z/AB= G/2A

Where A is the area of the triangle ABC.(10)

Q4: State and Prove “Converse theorem of force and a couple”?(10)

Q5: A rigid body or a set of rigid bodies, subject to workless constraints is in equilibrium iff zero virtual work is done by the applied forces and applied torques in any arbitrary infinitesimal displacement consistent with the constraints?(10)

### Mechanics-I Final 2021

. Find the center of mass of solid sphere

Q. No. 1

Calculate work done in vibration of a spring obeying Hooks law Briefly explain the work-energy theorem

Q. No. 2

Calculate the velocity and acceleration of many particles system at center of mass

Q. No. 3

Define In-elastic Collison and explain it in one dimension.

Calculate the center of mass of solid cylinder

Q.No. 4 Define elastic collision and explain elastic collision in two dimensions Q. No. 5 What do you know about conservative systems? Prove that the mass spring system is a conservative system.