A body is at rest at $x = 0$. At $t = 0$, it starts moving in the positive $x$-direction with a constant acceleration. At the same instant another body passes through $x = 0$ moving in the positive $x$ direction with a constant speed. The position of the first body is given by $\mathrm { x } _ { 1 } ( \mathrm { t } )$ after time ' t ' and that of the second body by $x _ { 2 } ( t )$ after the same time interval. Which of the following graphs correctly describes $\left( x _ { 1 } - x _ { 2 } \right)$ as a function of time ' $t$ '? (1), (2), (3), (4) [see graphs in original]
A thin rod of length ' $L$ ' is lying along the $x$-axis with its ends at $x = 0$ and $x = L$. Its linear density (mass/length) varies with $x$ as $k\left( \frac { x } { L } \right) ^ { n }$, where $n$ can be zero or any positive number. If the position $x _ { \mathrm { CM } }$ of the centre of mass of the rod is plotted against ' $n$ ', which of the following graphs best approximates the dependence of $x _ { \mathrm { CM } }$ on $n$? (1), (2), (3), (4) [see graphs in original]
A block of mass 0.50 kg is moving with a speed of $2.00 \mathrm{~m/s}$ on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is (1) 0.16 J (2) 1.00 J (3) 0.67 J (4) 0.34 J
Consider a uniform square plate of side ' $a$ ' and mass ' $m$ '. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is (1) $\frac { 5 } { 6 } m a ^ { 2 }$ (2) $\frac { 1 } { 12 } m a ^ { 2 }$ (3) $\frac { 7 } { 12 } m a ^ { 2 }$ (4) $\frac { 2 } { 3 } m a ^ { 2 }$