Q- A 2 m tall cylindrical compressor of mass 100 kg and 50 cm in diameter (base) is placed on a large cart. If there is sufficient friction to avoid any sliding, what is the maximum acceleration of the cart on level road for which the compressor will not topple.

### Fiber Optics: Dual Core Cable

Q- The diagram shows the end of a fiber optic cable with core refractive index 1.5 and cladding refractive index 1.4

(a) Find the critical angle at which light in the core is just totally internally reflected at X.

(b) Find the angle of incidence at A for light which is just internally reflected in the cable.

(c) Calculate the speed of light in the core.

(d) What is the time taken for light to travel 1.0 km directly down the centre of the core?

(e) Find the longest time taken for light to traverse 1.0 km of cable by internal reflections.

### Standing Waves: Vibrating string

Q- Figure shows the standing wave on a string, oscillating at frequency f_{o}.

(a) How many antinodes will there be if the frequency is doubled to 2f_{o}.

(b) If the tension in the string is increased by a factor of four, for what frequency will the string continue to oscillate as a standing wave with three antinodes?

### Current Electricity: Kirchhoff's laws

Q- Find the mesh currents and the voltage V_{ab} for the given network. The source is the current source supplying a current of 3 A.

### Kinematics: Projectile Motion

Q- A rocket is fired at an angle of 60^{0} with horizontal and accelerates in a straight line at 25ms^{-2 }for 2.5s before the rocket motor stops and it eventually falls to the ground. Neglecting air resistance

(a) Make a labelled sketch of the rockets trajectory starting from the launch point. Include the numerical values of the horizontal and vertical velocity at the point where the rocket motor stops.

(b) How long after launch does the rocket hit the ground?

(C) How far does the rocket travel horizontally from the launch point?

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