JEE Main 2006 — Mechanics

A ball of mass $0.2 \mathrm{~kg}$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2 \mathrm{~m}$ which applying the force and the ball goes upto $2 \mathrm{~m}$ height further, find the magnitude of the force. Consider $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$

A body falling from rest under gravity passes a certain point $P$. It was at a distance of $400 \mathrm{~m}$ from $P, 4 \mathrm{~s}$ prior to passing through $P$. If $g=10 \mathrm{~m} / \mathrm{s}^2$, then the height above the point $\mathrm{P}$ from where the body began to fall is

A bomb of mass $16 \mathrm{~kg}$ at rest explodes into two pieces of masses of $4 \mathrm{~kg}$ and $12 \mathrm{~kg}$. The velocity of the $12 \mathrm{~kg}$ mass is $4 \mathrm{~ms}^{-1}$. The kinetic energy of the other mass is

A force of $-F \hat{k}$ acts on $O$, the origin of the coordinate system. The torque about the point $(1,-1)$

A mass of $\mathrm{M} \mathrm{kg}$ is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of $45^{\circ}$ with the initial vertical direction is

A particle located at $x=0$ at time $t=0$, starts moving along the positive $x$-direction with a velocity ' $v$ ' that varies as $v=\alpha \sqrt{x}$. The displacement of the particle varies with time as

A particle of mass $100 \mathrm{~g}$ is thrown vertically upwards with a speed of $5 \mathrm{~m} / \mathrm{s}$. the work done by the force of gravity during the time the particle goes up is

A player caught a cricket ball of mass $150 \mathrm{~g}$ moving at a rate of $20 \mathrm{~m} / \mathrm{s}$. If the catching process is completed in $0.1 \mathrm{~s}$, the force of the blow exerted by the ball on the hand of the player is equal to

A thin circular ring of mass $\mathrm{m}$ and radius $\mathrm{R}$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $M$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $\omega^{\prime}=$

A wire elongates by $\ell \mathrm{mm}$ when a load $\mathrm{W}$ is hanged from it. If the wire goes over a pulley and two weights $\mathrm{W}$ each are hung at the two ends, the elongation of the wire will be (in $\mathrm{mm}$ )

Consider a two particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the centre of mass through a distance $d$, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

Four point masses, each of value $\mathrm{m}$, are placed at the corners of a square $A B C D$ of side $\ell$. The moment of inertia through $A$ and parallel to $B D$ is

If the terminal speed of a sphere of gold (density $=19.5 \mathrm{~kg} / \mathrm{m}^3$ ) is $0.2 \mathrm{~m} / \mathrm{s}$ in a viscous liquid (density $=1.5 \mathrm{~kg} / \mathrm{m}^3$ ) of the same size in the same liquid.

The potential energy of a $1 \mathrm{~kg}$ particle free move along the $\mathrm{x}$-axis is given by $$ V(x)=\left(\frac{x^4}{4}-\frac{x^2}{2}\right) J $$ The total mechanical energy of the particle $2 \mathrm{~J}$. Then, the maximum speed (in $\mathrm{m} / \mathrm{s}$ ) is

Which of the following units denotes the dimensions $\mathrm{ML}^2 / \mathrm{Q}^2$, where $\mathrm{Q}$ denotes the electric charge?