A bullet of $'4\,g'$ mass is fired from a gun of mass $4 \,{kg}$. If the bullet moves with the muzzle speed of $50\, {ms}^{-1}$, the impulse imparted to the gun and velocity of recoil of gun are :
$0.4\, {kg} \,{ms}^{-1}, 0.1\, {ms}^{-1}$
$0.2 \,{kg} \,{ms}^{-1}, 0.1\, {ms}^{-1}$
$0.2 \,{kg} \,{ms}^{-1}, 0.05\, {ms}^{-1}$
$0.4 \,{kg}\, {ms}^{-1}, 0.05 \,{ms}^{-1}$
A cannon ball is fired with a velocity $200\, m/sec$ at an angle of $60^o$ with the horizontal. At the highest point of its flight it explodes into $3$ equal fragments, one going vertically upwards with a velocity $100\, m/sec$, the second one falling vertically downwards with a velocity $100\, m/sec$. The third fragment will be moving with a velocity
An object of mass $3\,m$ splits into three equal fragments. Two fragments have velocities $v\hat j$ and $v\hat i$. The velocity of the third fragment is
A body of mass $m_1$ moving with an unknown velocity of $v_1 \hat i$ undergoes a collinear collision with a body of mass $m_2$ moving with a velocity $v_2 \hat i$ . After collision $m_1$ and $m_2$ move with velocities of $v_3 \hat i$ and $v_4 \hat i$ respectively. If $m_2 = 0.5\, m_1$ and $v_3 = 0.5\, v_1$ then $v_1$ is:
A $100\, kg$ gun fires a ball of $1\, kg$ horizontally from a cliff of height $500 \,m $. It falls on the ground at a distance of $400 \,m $ from bottom of the cliff. Find the recoil velocity of the gun. (acceleration due to gravity $g = 10\,ms^{-1}$ )
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}}$