**[OBJECTIVE]**

**Subject:** Mechanics

**Time Allowed:** 15 Minutes

**Maximum Marks:** 10

**NOTE:** *Attempt this Paper on this Question Sheet only. Please encircle the correct option. Division of marks is given in front of each question. This Paper will be collected back after expiry of time limit mentioned above.*

__Part-I Encircle the right answer, cutting and overwriting are not allowed. (10)__

- The moment of inertia of a spherical shell of mass M and radius a about ite diameter is

M/2a^{2}

3M/2a^{2}

2M/3a^{2}

2M/5a^{2}

2. Calculate gyroscopic couple acting on & disc which has radius of 135 mm. Angular and precessional velocities are 15 rad/sec and 7 rad/sec respectively. Assume density = 7810 kg/m^{3} and thickness of disc = 30 mm.

12.83 N-m

10.99N-m

11 N-m

Incomplete data

3. Total angular momentum of a body is given by

I x w where I: moment of inertia of body, w: angular velocity

I^{2} x w where I: moment of inertia of body, w: angular velocity

I^{2} x w^{2} where I: moment of inertia of body, w: angular velocity

I x w^{2} where I: moment of inertia of body, w: angular velocity

4. The Parallel-Axis theorem can be applied to determine

only the Moment of Inertia

only the Mass Moment of Inertia

both the Moment of Inertia and Mass Moment of Inertia

none of the above

5. The force -2 m W x V_{R1} called

Corlious force

Centrifugal force

Transverse force

Acceleration

6. The moment of inertia of a body is always minimum with respect to its

Base

Centroidal axis

Vertical axis

Horizontal axis

7. Apparent acceleration is measured in ________ frame [s) of reference.

fixed

rotating

both

none

8. Equation of momental ellipsoid of a solid cube at its center represents 8

Cube

Angular box

Both

None

9. (1 mark) A surface having no thickness is called

Ellipsoid

Cuboid

Lamina

Sphere

10. w x (w x r) is called ____________ acceleration.

centripetal

angular

Coriolis

none

**[SUBJECTIVE]**

**Subject:** Mechanics

**Time Allowed:** 2 Hours 45 Minutes

**Maximum Marks:** 50

**NOTE:** *ATTEMPT THIS (SUBJECTIVE) ON THE SEPARATE ANSWER SHEET PROVIDED.*

__Part-II Give short notes on following, each question carries equal marks. (20)__

**Q#1:** Define equimomental systems.

**Q#2:** Find M.I of rod of mass M and length 2L about a line through end points and per-pendicular to rod.

**Q#3:** In the absence of external torque, write down the Euler’s equations.

**Q#4:** Write down the necessary and sufficient conditions for two systems 5}, 52 to be equimo-mental.

**Q#5:** Write down the formula for product of Inertia about x, z-axes.

**Q#6:** Define inertia and write its units.

**Q#7:** State parallel axis theorem.

**Q#8:** Prove the principal of angular momentum for e rigid body rotating about 8 fixed axis.

**Q#9:** A rigid body has its three routually perpendicular axes of syrametry meeting at common point P. What do you know about principal axes of this body at point P.

**Q#10:** Differentiate between inertial and non-inertial frames of reference.

__Part-III Give detailed answers, each question carries equal marks. (30)__

**Q#1:** {a) – What is a spinning top? Express the equations for the motion of a spinning top having one point fixed on its axis in terms of Euler angles and find the condition of sleeping top.

(b) Find the moment of Inertia of a triangular lamina of mass M about one of its sides.

**Q#2:** (a) Show that rigid body motion is screw motion.

(b) Find the minimum spin of the gyroscope in above part 80 that it can sleep in the vertical position.

**Q#3:** (a) Discuss Torque free motion of a rigid body symmetric about an axis with one point fixed.

(b) State and prove CHASLE’s theorem.