A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor ?

A bullet of mass 0.04 kg moving with a speed of 90 ms^-1 enters a heavy wooden block and is stopped after a distance of 60 cm. What is the average resistive force exerted by the block on the bullet?

Anvils made of single crystals of diamond, with the shape as shown in Fig. 9.14, are used to investigate behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of 0.50 mm, and the wide ends are subjected to a compressional force of 50,000 N. What is the pressure at the tip of the anvil?:

A brass rod of length 50 cm and diameter 3.00 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250^@C , if the original lengths are at 40.0^@C ? Is there a 'thermal stress' developed at the junction? The ends of the rod are free to expand coefficent of linear expansion of brass = 2.0 xx 10^-5 ^@C^-1 , steel = 1.2 xx 10^-5 ^@C^-1 ).

A spring balance has a scale that readsfrom 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body ?

Figure 5.18 shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m s^-2 . What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt ? (Mass of the man = 65 kg.)

A current balance is a device to measure magnetic forces. It is constructed from two parallel coils, each with an average radius of 12.5 cm. The lower coil rests on a balance, it has 20 turns and carries a constant current of 4.0 A. The upper coil, suspended 0.314 cm above the lower coil, has 50 turns and a current that can be varied. The reading of the balance changes as the. magnetic force on the lower coil changes. What current is needed in the upper coil to exert a force of 1.0 N on the bottom coil?

A mass of 2 kg is attached to the spring of spring constant 50 N m^-1 . The lock is pulled to a distance of 5 cm from its equilibrium position at x = 0 on a horizontal frictionless surface from rest at t = 0. Write the expression for tis displacement at anytime t.

A circular coil of 16 turns and radius 10 cm carrying a current of 0.75 A rests with its plane normal to an external field of magnitude 5.0 xx 10^-2 T. The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of 2.0 s^-1 . What is the moment of inertia of the coil about its axis of rotation?