Question

te: Attempt all questions. Symbols have their usual meanings. The marks for each

question are indicated against it.

1. A box of mass 50 kg is placed on an inclined plane. When the angle of the plane is

increased to 30º, the box begins to slide downwards. Calculate the coefficient of static

friction between the plane and the box. Draw the free body diagram. (10)

2. A bullet of mass 20 g, travelling at a speed of 350 ms−1

, strikes a steel plate at an angle

of 30º with the plane of the plate. It ricochets off at the same angle, at a speed of

320 ms−1

. What is the magnitude of the impulse that the steel plate gives to the

projectile? If the collision with the plate takes place over a time ∆t = 10−3 s, what is the

average force exerted by the plate on the bullet? (10)

3. A truck of mass 2000 kg moving on a highway experiences an average frictional force

of 800 N. If its speed increases from 25 ms−1

to 35 ms−1

over a distance of 500 m,

what is the force generated by the truck. (10)

4. An automobile travelling at 80 km hr−1

has tyres of radius 80 cm. On applying brakes,

the car is brought to a stop in 30 complete turns of the tyres. What is the magnitude of

the angular acceleration of the wheels? How far does the car move while the brakes are

applied? (10)

5. An insect of mass 20 g crawls from the centre to the outside edge of a rotating disc of

mass 200g and radius 20 cm. The disk was initially rotating at 22.0 rads−1

. What will be

its final angular velocity? What is the change in the kinetic energy of the system? (10)

6. The position vector of two particles of mass 4.0 kg and 2.0 kg are, respectively,

r i j kˆ 2

ˆ ˆ 3

2

1 = t + t + t

r

and r i ( )j kˆ 4

ˆ 1

ˆ 3

2

2 = + t − + t

r

where t is in seconds and the position

in metres. Determine the position vector of the centre of mass of the system, the

velocity of the cm and the net force acting on the system. (10)

7. A solid cylinder of mass 3.0 kg and radius 1.0 m is rotating about its axis with a speed

of 40 rad s−1

. Calculate the torque which must be applied to bring it to rest in 10s. What

would be the power required? (10)

8. A proton undergoes a head on elastic collision with a particle of unknown mass which

is initially at rest and rebounds with 16/25 of its initial kinetic energy. Calculate the

ratio of the unknown mass with respect to the mass of the proton. (10)

9. A satellite going around Earth in an elliptic orbit has a speed of 10 km s−1

at the perigee

which is at a distance of 227 km from the surface of the earth. Calculate the apogee

distance and its speed at that point.

Answer 1

m = 20 grams = 0.02 kg

Impulse = J = mΔv

J =m * (Vf - Vi)
J = 0.02*( 320@30 - 350@330)
J = 0.02*( 320@30 + 350@150)
OR:
J = 6.4@30 + 7@150

∑Px
6.4* Cos( 30)+ 7* Cos(150) = -0.5196 kg*m/s

∑Py
6.4* Sin( 30)+ 7* Sin(150) = 6.7kg*m/s

Bullet Impulse magnitude sqr(Px^2+Py^2) = 6.720 kg*m/s