JEE (Advanced) 2007 Paper-2

In the experiment to determine the speed of sound using a resonance column,

A student performs an experiment to determine the Young’s modulus of a wire, exactly 2 m long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of $$\pm 0.05$$ mm at load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of $$\pm 0.01$$ mm. Take g = 9.8 m/s$$^2$$ (exact). The Young’s modulus obtained from the reading is

A particle moves in the X-Y plane underthe influence of a force such that its linear momentum is $$\overrightarrow{p}(t) = A\left[\hat{i} \cos (kt) - \hat{j} \sin (kt)\right]$$, where A and k are constants. The angle between the force and the momentum is

A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of $$\frac{3v^2}{4g}$$ with respect to the initial position. The object is

Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is $$\rho$$, the surface tension of water is T and the atmospheric pressure is $$P_0$$. Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude.

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as showing the figure. The electric field inside the emptied space is

Positive and negative point charges of equal magnitude are kept at $$\left(0, 0, \frac{a}{2}\right)$$ and $$\left(0, 0, \frac{-a}{2}\right)$$, respectively. The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is

A magnetic field $$\overrightarrow{B} = B_0\hat{j}$$ exists in the region a < x < 2a and $$\overrightarrow{B} = -B_0 \hat{j}$$, in the region 2a < x < 3a, where $$B_0$$ is a positive constant. A positive point charge moving with a velocity $$\overrightarrow{v} = v_0 \hat{i}$$, where $$v_0$$ is a positive constant, enters the magnetic field at x = a. The trajectory of the charge in this region can be like,

Electrons with de-Broglie wave length $$\lambda$$ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

STATEMENT-1
If there is no external torque on a body aboutits center of mass, then the velocity of the center of mass remains constant.
because
STATEMENT-2
The linear momentum of an isolated system remains constant.