JEE Main 2009 — Mechanics

The height at which the acceleration due to gravity becomes $\frac{\mathrm{g}}{9}$ (where $\mathrm{g}=$ the acceleration due to gravity on the surface of the earth) in terms of $R$, the radius of the earth is

A particle has an initial velocity $3 \hat{i}+4 \hat{j}$ and an acceleration of $0.4 \hat{i}+0.3 \hat{j}$. Its speed after 10 s is

A thin uniform rod of length $\ell$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of

Consider a rubber ball freely falling from a height $h=4.9 \mathrm{~m}$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time the height as function of time will be

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree $\left(=0.5^{\circ}\right)$, then the least count of the instrument is

Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area $A$ and wire-2 has cross-sectional area $3 A$. If the length of wire 1 increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire 2 by the same amount?