The velocity of a small ball of mass '$$M$$' and density '$$\mathrm{d}_1$$' when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is '$$\mathrm{d}_2$$', the viscous force acting on the ball is ( $$\mathrm{g}=$$ acceleration due to gravity)

A sphere of mass 25 gram is placed on a vertical spring. It is compressed by $$0.2 \mathrm{~m}$$ using a force $$5 \mathrm{~N}$$. When the spring is released, the sphere will reach a height of $$\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$$ $$2 \mathrm{~m}$$

A bomb is dropped by an aeroplane flying horizontally with a velocity $$200 \mathrm{~km} / \mathrm{hr}$$ and at a height of $$980 \mathrm{~m}$$. At the time of dropping a bomb, the distance of the aeroplane from the target on the ground to hit directly is $$\left(g=9.8 \mathrm{~m} / \mathrm{s}^2\right)$$

A series combination of resistor 'R' and capacitor 'C' is connected to an a.c. source of angular frequency '$$\omega$$'. Keeping the voltage same, if the frequency is changed to $$\frac{\omega}{3}$$ the current becomes half of the original current. Then the ratio of capacitive reactance and resistance at the former frequency is