1
IIT-JEE 2011 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision, A
the ring has pure rotation about its stationary CM.
B
the ring comes to a complete stop.
C
friction between the ring and the ground is to the left.
D
there is no friction between the ring and the ground.
2
IIT-JEE 2008 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

Two balls, having linear momenta $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$$, undergo a collision in free space. There is no external force acting on the balls. Let $${\overrightarrow {p'} _1}$$ and $${\overrightarrow {p'} _2}$$ be their final momenta. The following option(s) is (are) NOT ALLOWED for any non-zero value of $$p,{a_1},{a_2},{b_1},{b_2},{c_1}$$ and $${c_2}$$ :

A
$${\overrightarrow {p'} _1} = {a_1}\widehat i + {b_1}\widehat j + {c_1}\widehat k;{\overrightarrow {p'} _2} = {a_2}\widehat i + {b_2}\widehat j$$
B
$${\overrightarrow {p'} _1} = {c_1}\widehat k;{\overrightarrow {p'} _2} = {c_2}\widehat k$$
C
$${\overrightarrow {p'} _1} = {a_1}\widehat i + {b_1}\widehat j + {c_1}\widehat k;{\overrightarrow {p'} _2} = {a_2}\widehat i + {b_2}\widehat j - {c_1}\widehat k$$
D
$${\overrightarrow {p'} _1} = {a_1}\widehat i + {b_1}\widehat j;{\overrightarrow {p'} _2} = {a_2}\widehat i + {b_2}\widehat j$$
3
IIT-JEE 1998 Screening
MCQ (More than One Correct Answer)
+2
-0.5
A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the center. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is
A
$$\sqrt {{u^2} - 2gL}$$
B
$$\sqrt {2gL}$$
C
$$\sqrt {{u^2} - gL}$$
D
$$\sqrt {2\left( {{u^2} - gL} \right)}$$
4
IIT-JEE 1998 Screening
MCQ (More than One Correct Answer)
+2
-0.5
A force $$F = - K\left( {y\widehat i + x\widehat j} \right)$$ (where K is a positive constant) acts on a particle moving in the xy plane. Starting from the origin, the particle is taken along the positive x axis to the point $$\left( {a,0} \right)$$, and then parallel to the y axis to the point $$\left( {a,a} \right)$$. The total work done by the force F on the particle is
A
$$- 2K{a^2}$$
B
$$2K{a^2}$$
C
$$- K{a^2}$$
D
$$K{a^2}$$
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