A company sells biscuitws. For packing purpose they are using cuboidal boxes : box `A rarr 3 cm xx 8 cm xx 20 cm, box B rarr 4 cm xx 12 cm xx 10 cm`. What size of the box will be econmical for the company? Why? Can you suggest any other size (dimensions) which has the sdame volumne but is more economical than these?

A 5m 60 cm high vertical pole caste a shadow 3m 20 cm long. Find at the same time (i) the length of the shadow cast by another pole 10 m 50 cm high (ii) the height of apole which caste a shadow 5m long.

A spherical conductor of radius 12 cm has a charge 1.6xx10^(-7) C distributed uniformly on its surface. What is the electric filed inside the sphere

Two spheres of radii 3cm and 8cm are charged with 4xx10^(-9)C and 1.6xx10^(-9)C of electricity respectively. If they are joined by a wire, how much charge will flow from one to the other sphere?

A spherical conductor of radius 12 cm has a charge 1.6xx10^(-7) C distributed uniformly on its surface. What is the electric filed outside the sphere.

A farmer connects a pipe of internal diameter 20cm from a canal into a cylindrical tank in her field,which is 10 m in diameter and 2 m deep.If water flows through thr pipe at the rate of 3 km/h,in how much time will the tank be filled?

A large steel wheel is to be fitted on to a shaft of the same material. At 27 ^@C , the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range: a_ steel = 1.20 xx 10^-5K^-1 .

A brass rod of length 50 cm and diameter 3.0 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 (Co-efficient of linear expansion of brass = 2.0 xx 10^-5K^-1 steel = 1.2 xx 10^-5 K^-1) .