1
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is

A
$${{2GM} \over {7R}}(4\sqrt 2 - 5)$$
B
$$- {{2GM} \over {7R}}(4\sqrt 2 - 5)$$
C
$${{GM} \over {4R}}$$
D
$${{2GM} \over {5R}}(\sqrt 2 - 1)$$
2
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-0

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
$$\mathrm{(A)\to (T),(S);(B)\to (Q),(T);(C)\to(P),(R),(T);(D)\to(Q)}$$
B
$$\mathrm{(A)\to (T),(P);(B)\to (Q),(S),(T);(C)\to(P),(R),(T);(D)\to(Q)}$$
C
$$\mathrm{(A)\to (T),(Q);(B)\to (Q),(S),(T);(C)\to(P),(R),(T);(D)\to(S)}$$
D
$$\mathrm{(A)\to (P);(B)\to (S),(T);(C)\to(P),(R),(T);(D)\to(T)}$$
3
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

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

A
B
C
D
4
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

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'.

A
Statement - 1 is True, Statement - 2 is True; Statement - 2 is a correct explanation for Statement - 1
B
Statement - 1 is True, Statement - 2 is True; Statement - 2 is NOT a correct explanation for Statement - 1
C
Statement - 1 is True, Statement - 2 is False
D
Statement - 1 is False, Statement - 2 is True
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