Column II shows five systems in which two objects are labelled as X and Y. Also in each case a point P is shown. Column I gives some statements about X and/or Y. Match these statements to the appropriate system(s) from Column II:
| Column I | Column II | ||
|---|---|---|---|
| (A) | The force exerted by X on Y has a magnitude $$Mg$$. | (P) |  Block Y of mass M left on a fixed inclined plane X, slides on it with a constant velocity. |
| (B) | The gravitational potential energy of X is continuously increasing. | (Q) |  Two rings magnets Y and Z, each of mass M, are kept in frictionless vertical plastic stand so that they repel each other. Y rests on the base X and Z hangs in air in equilibrium. P is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity. |
| (C) | Mechanical energy of the system X + Y is continuously decreasing. | (R) |  A pulley Y of mass $$m_0$$ is fixed to a table through a clamp X. A block of mass M hangs from a string that goes over the pulley and is fixed at point P of the table. The whole system is kept in a lift that is going down with a constant velocity. |
| (D) | The torque of the weight of Y about point is zero. | (S) |  A sphere Y of mass M is put in a non-viscous liquid X kept in a container at rest. The sphere is released and it moves down in the liquid. |
| (T) | A sphere Y of mass M is falling with its terminal velocity in a viscous liquid X kept in a container. |
A spherically symmetric gravitational system of particles has a mass density
$$\rho = \left\{ {\matrix{ {{\rho _0}} & {for} & {r \le R} \cr 0 & {for} & {r > R} \cr } } \right.$$
Where $$\rho_0$$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance $$r(0 < r < \infty)$$ from the centre of the system is represented by
STATEMENT - 1
An astronaut in an orbiting space station above the Earth experiences weightlessness.
and
STATEMENT - 2
An object moving around the Earth under the influence of Earth's gravitational force is in a state of 'free-fall'.
Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 $$\times$$ 4 matrix given in the ORS.
| Column I | Column II | ||
|---|---|---|---|
| (A) | GM$$_e$$M$$_s$$ G - universal gravitational constant, M$$_e$$ - mass of the earth, M$$_s$$ - mass of the Sun |
(P) | (volt) (coulomb) (metre) |
| (B) | $${{3RT} \over M}$$ R - universal gas constant, T - absolute temperature, M - molar mass |
(Q) | (kilogram) (metre)$$^3$$ (second)$$^{-2}$$ |
| (C) | $${{{F^2}} \over {{q^2}{B^2}}}$$ F - force, q - charge, B - magnetic field |
(R) | (metre)$$^2$$ (second)$$^{-2}$$ |
| (D) | $${{G{M_e}} \over {{R_e}}}$$ G - universal gravitational constant, M$$_e$$ - mass of the earth R$$_e$$ - radius of the earth |
(S) | (farad) (volt)$$^2$$ (kg)$$^{-1}$$ |
JEE Advanced Subjects
Browse all chapters by subject