NCERT Solutions for Chapter: Laws of Motion, Exercise 5: LA

 Figure $\left(a\right)$and $\left(b\right)$ shows $\left(v_x, t\right)$ and $\left(v_y, t\right)$ diagrams for a body of unit mass. Find the force, as a function of time.

 A racing car travels on a track (without banking) $ABCDEFA$ (Figure). $ABC$ is a circular arc of radius $2R$. $CD$ and $FA$ are straight paths of length $R$ and $DEF$ is a circular arc of radius $R=100 m$. The coefficient of friction on the road is $\mu =0.1$. The maximum speed of the car is $50 {\text{ms}}^{-1}$. Find the minimum time for completing one round.

The displacement vector of a particle of mass $m$ is given by $\overrightarrow{r}\left(t\right)=\hat{i}A\cos \omega t+\hat{j}B\sin \omega t$

Show that the trajectory is an ellipse.

The displacement vector of a particle of mass $m$ is given by

$\overrightarrow{r}\left(t\right)=\hat{i}A\cos \omega t+\hat{ȷ}B\sin \omega t$

Show that $\overrightarrow{F}=-m{\omega }^2\overrightarrow{r}$

There are four forces acting at a point $P$ produced by strings as shown in the figure, which is at rest. Find the forces $F_1$and $F_2$.

 A helicopter of mass $2000 \mathrm{kg}$ rises with a vertical acceleration of $15 \mathrm{m} {\mathrm{s}}^{-2}$. The total mass of the crew and passengers is $500 \mathrm{kg}$. Give the magnitude and direction of the $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

Force on the floor of the helicopter by the crew and passengers.

 A helicopter of mass $2000 \mathrm{kg}$ rises with a vertical acceleration of $15 \mathrm{m} {\mathrm{s}}^{-2}$. The total mass of the crew and passengers is $500 \mathrm{kg}$. Give the magnitude and direction of the $(\mathrm{g}=$10 $10 {\text{m s}}^{-2}\text{)}$

The action of the rotor of the helicopter on the surrounding air.

 A helicopter of mass $2000 \mathrm{kg}$ rises with a vertical acceleration of $15 \mathrm{m} {\mathrm{s}}^{-2}$. The total mass of the crew and passengers is $500 \mathrm{kg}$. Give the magnitude and direction of the $(\mathrm{g}=$10 $10 {\text{m s}}^{-2}\text{)}$

Force on the helicopter due to the surrounding air.