JEE Advanced 2011 · Paper 2

A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is

1. A½ mV²
2. BmV²
3. C³⁄₂ mV²
4. D2mV²

A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x₁(t) = A sin ωt and x₂(t) = A sin(ωt + 2π/3). Adding a third sinusoidal displacement x₃(t) = B sin(ωt + φ) brings the mass to a complete rest. The values of B and φ are

1. A√2 A, 3π/4
2. BA, 4π/3
3. C√3 A, 5π/6
4. DA, π/3

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is

1. A0.9%
2. B2.4%
3. C3.1%
4. D4.2%

Which of the following statement(s) is/are correct?

1. AIf the electric field due to a point charge varies as r⁻²·⁵ instead of r⁻², then the Gauss law will still be valid.
2. BThe Gauss law can be used to calculate the field distribution around an electric dipole.
3. CIf the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.
4. DThe work done by the external force in moving a unit positive charge from point A at potential VA to point B at potential VB is (VB − VA).