A man is standing at the centre of frictionless pond of ice. How can he get himself to the shore
By throwing his shirt in vertically upward direction
By spitting horizontally
He will wait for the ice to melt in pond
Unable to get at the shore
The balls, having linear momenta $\vec{p}_1=\hat{p} \hat{i}$ and $\vec{p}_2=-p \hat{i}$, undergo a collision in free space. There is no external force acting on the balls. Let $\vec{p}_1^{\prime}$ and $\vec{p}_2^{\prime}$ be their final momenta. The following option$(s)$ is (are) $NOT ALLOWED$ for any non-zero value of $\mathrm{p}, \mathrm{a}_1, \mathrm{a}_2, \mathrm{~b}_1, \mathrm{~b}_2, \mathrm{c}_1$ and $\mathrm{c}_2$.
$(A)$ $ \overrightarrow{\mathrm{p}}_1^{\prime}=\mathrm{a}_1 \hat{\mathrm{i}}+\mathrm{b}_1 \hat{\mathrm{j}}+\mathrm{c}_1 \hat{\mathrm{k}} $
$ \overrightarrow{\mathrm{p}}_2^{\prime}=\mathrm{a}_2 \hat{\mathrm{i}}+\mathrm{b}_2 \hat{\mathrm{j}}$
$(B)$ $ \overrightarrow{\mathrm{p}}_1^{\prime}=\mathrm{c}_1 \hat{\mathrm{k}} $
$ \overrightarrow{\mathrm{p}}_2^{\prime}=\mathrm{c}_2 \hat{\mathrm{k}}$
$(C)$ $ \overrightarrow{\mathrm{p}}_1^{\prime}=\mathrm{a}_1 \hat{\mathrm{i}}+\mathrm{b}_1 \hat{\mathrm{j}}+\mathrm{c}_1 \hat{\mathrm{k}} $
$ \overrightarrow{\mathrm{p}}_2=\mathrm{a}_2 \hat{\mathrm{i}}+\mathrm{b}_2 \hat{\mathrm{j}}-\mathrm{c}_1 \hat{\mathrm{k}}$
$(D)$ $ \vec{p}_1^{\prime}=a_1 \hat{i}+b_1 \hat{j} $
$ \overrightarrow{\mathrm{p}}_2^{\prime}=a_2 \hat{\mathrm{i}}+b_1 \hat{\mathrm{j}}$
A jet engine works on the principle of
A projectile is fired with velocity $u$ at an angle $\theta$ with horizontal. At the highest point of its trajectory it splits up into three segments of masses $m, m$ and $2 \,m$. First part falls vertically downward with zero initial velocity and second part returns via same path to the point of projection. The velocity of third part of mass $2 \,m$ just after explosion will be
A body of mass $M$ at rest explodes into three pieces, in the ratio of masses $1: 1: 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \,ms ^{-1}$ and $40 \,ms ^{-1}$ respectively. The velocity of the third piece will be ............... $\,ms ^{-1}$
If final momentum is equal to initial momentum of the system then