# ### Momentum-Vector

Q- A 3.00 kg particle has a velocity of (3.00 i - 4.00 j) m/s.

(a) Find its x and y components of momentum.

(b) Find the magnitude and direction of its momentum.

### Electromagnetism: Moving Charge in a Magnetic Field

Q- In an experiment with cosmic rays, a vertical beam of particle that have charge of magnitude 3e and mass 12 times the proton mass enters a uniform horizontal magnetic field of 0.250 T and is bent in a semicircle of diameter 95.0 cm as shown in the diagram

(a) Find the speed of the particles and the sign of their charge.

(b) Is it reasonable to ignore the gravity force on the particles?

(c) How does the speed of the particles as they enter the field compare to their speed as they exit the field. Solution:

### Force And Torque: Toppling

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.

Solution:

### 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. Solution:

### Standing Waves: Vibrating string

Q- Figure shows the standing wave on a string, oscillating at frequency fo.

(a) How many antinodes will there be if the frequency is doubled to 2fo.

(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? Solution:

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