**Question 1:**

A 2 kg body moving to the right with speed 6 m/s coliides elastcally with a stationary body of mass 4 kg.

a.Find the velocity vector of each mass relative to center of mass before and after the collsion

b.Find the velocity vector of the each mass in original frame after the collision

c.How much energy was transfered to the 4 kg body.

Take i as the unit vector in the right direction

**Answer**

a.

Before collision

Velocity vector of mass 2 kg=4i m/s

Velocity vector of mass 4 kg=-2i m/s

After collision

Velocity vector of mass 2 kg=-4i m/s

Velocity vector of mass 4 kg=2i m/s

b

Velocity vector of mass 2 kg=-2i m/s

Velocity vector of mass 4 kg=4i m/s

c. 32 J

**Hints:**

Velocity of the center of mass=m

_{1}v

_{1}+m

_{2}v

_{2}/m

_{1}+m

_{2}

Velocity w.r.t CM=v-v

_{cm}

Applying law of linear momentum and energy conservation,veloclities after collosion could be find out

**Question 2:**

A small solid cylinder of radius r rolls down from the top of sphere of Radius R without slipping.

a. find the angle made from the vertical at which the cylinder loses contact with the surface of the sphere

b.find the angular velocity of the cylinder at the moment it loses contact with the surface of the sphere

**Answer**

a. cos

^{-1}(4/7)

b.(2/r)[(R+r)g/7]

^{1/2}

**hints:**

Normal reaction will become zero at the point of losing contact

so centripetal force will become equal to the weight components across the radius.

Also applying law of conservation of energy ...we can find the solution

**Question 3:**

An gas obeys Vander waal equation

(P+a/V

^{2})(V-b)=nRT

Find following for such a gas

A. The dimensional formula for constant a is

a.ML

^{5}T

^{-2}

b.ML

^{5}T

^{-1}

c.ML

^{-1}T

^{-1}

d. M

^{0}L

^{-0}T

^{0}

B. Find the workdone by this gas when gas expand from V to 2V at constant temperature T

a.nRTlog

_{e}(2V-b/V-b) -a/V

b.nRTlog

_{e}(2V-b/V-b) +a/V

c. nRTlog

_{e}(2V-b/V-b)

d. none of the above

C.Bulk modulus at constant pressure is defined as

K=(-1/V)(dP/dV)

_{T}

Find the value of k for this gas

a.(1-b/V)(p-a/V

^{2}+2a/V

^{3})

b. (1+b/V)(p-a/V

^{2}+2a/V

^{3})

c.(1-b/V)(p-a/V

^{2}-2a/V

^{3})

d.None of the above

**Answer:**

A.ML

^{5}T

^{-2}

B.nRTlog

_{e}(2V-b/V-b) -a/V

**Question 4:**

An electron (mass m and charge e) is moving along the axis of the ring of radius r and carrying a charge q.Find the time period of small oscillation of the electron about the center of the ring

**Answer**

T=4π(πε

_{0}mr

^{3}/eq)

^{1/2}

**Hint:**

Electric field at a point on the axis of the ring at the distance x from its center is

E=qx/4πε

_{0}(r

^{2}+x

^{2})

^{3/2}

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