Suppose that a mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the diameter of the ball decreases from 2cm to 1cm in 3 months, how long will it take until the ball has practically gone?

Three smaller circular balls are made by melting a copper spherical ball of radius 3 cm.If the diameter of first two smaller balls be 1.5 cm and 2 cm respectively, then what will be the diameter of third ball?

The diameter of a lead ball is 2.1 cm The density of the lead used is 11.34 g//c^(3) What is the weight of the ball ?

Water is pouring into a conical vessel of diameter 5.2m. And slant height 6.8 m(as shown in the adjoining ) , at the rate of 1.8 m^(3) per minute .How long will it take to fill the vessel?

A spherical ice ball melts in such a way that the rate of melting is proportional to its volume of ice at that instant. If half the quantity of ice melts in 30 minutes, show that after 90 minutes from the start of melting, the volume of ice that remains is (1)/(8) time of the original volume of the ice ball.

Water flows at the rate of 10 m/min from a cylinderical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm ?

A ball is thrown vertically upwards with a velocity of 20 ms^(-1) from the top of a multistorey building. The height of the point from where the ball is thrown is 25.0 m from the ground. (a) How high will the ball rise ? and (b) how long will it be before the ball hits the ground ? Take g = 10 ms^(-2) .

When an air bubble rises from the bottom of a lake to the upper surface , its diameter increases from 1mm to 2mm. IF the atmospheric pressure is 76 cmHg,calculate the depth of the lake. Density of mercury is 13.6g.cm^-3 .

A ladder 5 cm long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 cm away from the wall ?

A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the mef developed across the cut if the velocity of the loop is 1 m. s^(-1) in a direction normal to the Suppose in this case the loop is stationary but the current feeding the electromagnet produces the magnetic field is gradually reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 T. s^(-1) . If the cut is joined and the loop has a resistance of 1.6 Omega , how much power is dissipated by the loop as heat? What is the source of this power?