1
JEE Advanced 2018 Paper 2 Offline
+3
-0.75
In the List-$${\rm I}$$ below, four different paths of a particle are given as functions of time. In these functions, $$\alpha$$ and $$\beta$$ are positive constants of appropriate dimensions and $$\alpha \ne \beta$$ In each case, the force acting on the particle is either zero or conservative. In List-$${\rm I}{\rm I}$$, five physical quantities of the particle are mentioned $$\overrightarrow p$$ is the linear momentum, $$\overrightarrow L$$ is the angular momentum about the origin, $$K$$ is the kinetic energy, $$U$$ is the potential energy and $$E$$ is the total energy. Match each path in List-$${\rm I}$$ with those quantities in List-$${\rm II}$$, which are conserved for that path.

LIST - I LIST - II
P. $$\overrightarrow r$$(t)=$$\alpha$$ $$t\,\widehat i + \beta t\widehat j$$ 1. $$\overrightarrow p$$
Q. $$\overrightarrow r \left( t \right) = \alpha \cos \,\omega t\,\widehat i + \beta \sin \omega t\,\widehat j$$ 2. $$\overrightarrow L$$
R. $$\overrightarrow r \left( t \right) = \alpha \left( {\cos \omega t\,\widehat i + \sin \omega t\widehat j} \right)$$ 3. K
S. $$\overrightarrow r \left( t \right) = \alpha t\,\widehat i + {\beta \over 2}{t^2}\widehat j$$ 4. U
5. E
A
$$P \to 1,2,3,4,5;\,Q \to 2,5;R \to 2,3,4,5;S \to 5$$
B
$$P \to 1,2,3,4,5;{\mkern 1mu} Q \to 3,5;R \to 2,3,4,5;S \to 2,5$$
C
$$P \to 2,3,4;{\mkern 1mu} Q \to 5;R \to 1,2,4;S \to 2,5$$
D
$$P \to 1,2,3,4,5;{\mkern 1mu} Q \to 2,5;R \to 2,3,4,5;S \to 2,5$$
2
JEE Advanced 2015 Paper 1 Offline
+8
-4

A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in Column I (a and U0 are constants). Match the potential energies in Column I to the corresponding statement(s) in Column II: A
(A)→(P), (Q), (R); (B)→(Q), (S); (C)→(P), (Q), (R), (S); (D)→(P), (R), (T)
B
(A)→(P), (Q), (R), (T); (B)→(Q), (S); (C)→(P), (Q), (R), (S); (D)→(P), (R), (T)
C
(A)→(P), (Q), (R), (T); (B)→(Q); (C)→(P), (Q), (R), (S); (D)→(P), (R), (T)
D
(A)→(P), (Q), (R), (T); (B)→(Q), (S); (C)→(P), (Q), (R), (S); (D)→(P), (R)
3
JEE Advanced 2014 Paper 2 Offline
+3
-0.75
A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy K with time t most appropriately? The figures are only illustrative and not to the scale.
A B C D 4
JEE Advanced 2013 Paper 2 Offline
+3
-0.75

A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, below, is 150 J. (Take the acceleration due to gravity, g = 10 m/s2) The speed of the block when it reaches the point Q is

A
5 ms-1
B
10 ms-1
C
$$10\sqrt 3$$ ms-1
D
20 ms-1
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