31.

Copy and complete the following nuclear equations by filling in the correct values in the blanks:

State Newton’s second law of motion both in words and in equation form. Under what condition does this equation become F = ma?

The radius of the driving wheel of a set of gears is 18 cm. It has 100 teeth and rotates at a speed of 30 rpm. The driven wheel rotates at a speed of 150 rpm. Calculate:

i) the gear ratio; ii) the number of teeth on the driven wheel and iii) the radius of the driven wheel. 

A small stone of mass m = 200 g is held under water in a tall jar and is allowed to fall as shown in the figure. The free body diagram of the stone is also shown:

 

i) What do F₂ and m₁ represent?

ii) Calculate the net force acting on the stone and

iii) its acceleration as it falls through water. (Neglect the force due to viscosity. Take the volume of the stone as 80 cm³, density of water as 1.0 g/cm³ and acceleration due to gravity, g = 10 m/s². 

A thermos flask of negligible heat capacity contains 100 g of ice and 30 g of water.

i) Calculate:

1. the mass of steam of 100⁰ C needed to condense in the flask so as to just melt the ice.

2. the amount of water in the flask after condensation.

(Specific latent heat of vaporisation of the steam = 2260 J/g

Specific latent heat of fusion of ice = 336 J/ g

Specific heat capacity of water = 4.2 J.g⁰C)

i) State the principle of calorimetry.

ii) Express 1 k/wh in terms of S.I. unit of energy.

An electric bulb rated 220 V, 60 W is working at full efficiency.

i) State the resistance of the coil of the bulb.

ii) Another identical bulb is connected in series with the first one and the system is connected across the mains as shown alongside:

1. State the rate of conversion of energy in each bulb.
2. Calculate the total power.