JEE Main 2008 — Mechanics

A block of mass $0.50 \mathrm{~kg}$ is moving with a speed of $2.00 \mathrm{~m} / \mathrm{s}$ on a smooth surface. It strikes another mass of $1.00 \mathrm{~kg}$ and then they move together as a single body. The energy loss during the collision is

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 ' $\mathrm{t}$ ' 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 ' $t$ '?

A body of mass $m=3.513 \mathrm{~kg}$ is moving along the $x$-axis with a speed of $5.00 \mathrm{~ms}^{-1}$. The magnitude of its momentum is recorded as

A capillary tube $(\mathrm{A})$ is dropped in water. Another identical tube $(\mathrm{B})$ is dipped in a soap water solution. Which of the following shows the relative nature of the liquid columns in the two tubes? 

A jar filled with two non mixing liquids 1 and 2 having densities $\rho_1$ and $\rho_2$ respectively. A solid ball, made of a material of density $\rho_3$, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $\rho_1, \rho_2$ and $\rho_3$ ? 

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is $11 \mathrm{kms}^{-1}$, the escape velocity from the surface of the planet would be

A spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2\left(\rho_2 < \rho_1\right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., $F_{\text {viscous }}=-k v^2(k>0)$. The terminal speed of the ball is

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 $x$ ask $\left(\frac{x}{L}\right)^n$, 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 $n$ ?

An athlete in the olympic games covers a distance of $100 \mathrm{~m}$ in $10 \mathrm{~s}$. His kinetic energy can be estimated to be in the range

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

Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer.  The value of the unknown resistor $R$ is

The dimension of magnetic field in $\mathrm{M}, \mathrm{L}, \mathrm{T}$ and $\mathrm{C}$ (Coulomb) is given as

This question contains Statement $-1$ and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement - I: For a mass $M$ kept at the centre of a cube of side ' $a$ ', the flux of gravitational field passing through its sides is $4 \pi$ GM. and Statement - II If the direction of a field due to a point source is radial and its dependence on the distance ' $r$ ' for the source is given as $1 / r^2$, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface

Two full turns of the circular scale of a screw gauge cover a distance of $1 \mathrm{~mm}$ on its main scale. The total number of divisions on the circular scale is 50 . Further, it is found that the screw gauge has a zero error of $-0.03 \mathrm{~mm}$ while measuring the diameter of a thin wire, a student notes the main scale reading of $3 \mathrm{~mm}$ and the number of circular scale divisions in line with the main scale as 35 . The diameter of the wire is