Competitive Thinking

When a body is moving on a surface, the force of friction is called

The speed of the wind passing over the wings of a small aeroplane is $70 \mathrm{m} {\mathrm{s}}^{-1}$ and below the wing is $60 \mathrm{m} {\mathrm{s}}^{-1}$. If the mass of the plane is $1000$ $\mathrm{kg}$ and the area of wing is $14 {\mathrm{m}}^2$, then, what will be the net vertical force on the aeroplane? (Density of air$=1.2 \mathrm{kg} {\mathrm{m}}^{-3}$ and $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A rectangular vessel when full of water takes $10 \min$ to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water?

A vessel completely filled with water has holes $A$ and $B$ at depths $\mathrm{h}$ and $3\mathrm{h}$ from the top respectively. Hole $A$ is a square of side $L$ and $B$ is circle of radius$r$. The water flowing out per second from both the holes is same. Then, $L$ is equal to

A large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water, the quantity of water flowing out per second from both the holes are the same. Then, $R$ is equal to

A body of mass $2 \mathrm{kg}$ is being dragged with uniform velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$ on a rough horizontal plane. The coefficient of friction between the body and the surface is $0.20$. The amount of heat generated in $5 \mathrm{s}$ is $\left(1 \mathrm{J}=4.2 \mathrm{cal} \mathrm{and} g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A spherical solid ball of volume $V$ is made of a material of density ${\rho }_1$. It is falling through a liquid of density ${\rho }_2,\left({\rho }_2<{\rho }_1\right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $\mathrm{v}$, i.e., $F_{\mathrm{viscous} }=-k{v}^2 \left(k>0\right)$. The terminal speed of the ball is

The heart of a man pumps $5 \mathrm{liters}$ of blood through the arteries per minute at a pressure of $150 \mathrm{mm}$ of mercury. If the density of mercury be $13.6\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ and $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$, then, the power of heart in $\mathrm{watt}$ is