1
JEE Advanced 2017 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-0.75
Change Language
Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $$\rho $$ remains uniform throughout the volume. The rate of fractional change in density $$\left( {{1 \over \rho } {{d\rho } \over {dt}}} \right)$$ is constant. The velocity $$v$$ of any point on the surface of the expanding sphere is proportional to
A
$$R$$
B
$${R^3}$$
C
$${1 \over R}$$
D
$${R^{2/3}}$$
2
JEE Advanced 2017 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-0.75
Change Language
Three vectors $$\overrightarrow P ,\overrightarrow Q $$ and $$\overrightarrow R $$ are shown in the figure. Let $$S$$ be any point on the vector $$\overrightarrow R .$$ The distance between the points $$P$$ and $$S$$ is $$b\left| {\overrightarrow R } \right|.$$ The general relation among vectors $$\overrightarrow P ,\overrightarrow Q $$ and $$\overrightarrow S $$ is :

JEE Advanced 2017 Paper 2 Offline Physics - Motion Question 7 English
A
$$\overrightarrow S = \left( {1 - b} \right)\overrightarrow P + b\overrightarrow Q $$
B
$$\overrightarrow S = \left( {b - 1} \right)\overrightarrow P + b\overrightarrow Q $$
C
$$\overrightarrow S = \left( {1 - {b^2}} \right)\overrightarrow P + b\overrightarrow Q $$
D
$$\overrightarrow S = \left( {1 - b} \right)\overrightarrow P + {b^2}\overrightarrow Q $$
3
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
STATEMENT-1: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

STATEMENT-2: If the observer and the object are moving at velocities $${\overrightarrow v _1}$$ and $${\overrightarrow v _2}$$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $${\overrightarrow v _2}$$ - $${\overrightarrow v _1}$$.

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
4
IIT-JEE 2007 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

A fixed thermally conducting cylinder has a radius $R$ and height $L_0$. The cylinder is open at its bottom and has a small hole at its top. A piston of mass $M$ is held at a distance $L$ from the top surface, as shown in the figure. The atmospheric pressure is $P_0$.

IIT-JEE 2007 Paper 1 Offline Physics - Motion Question 3 English Comprehension

While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is :

A
$$\left( {{{2{P_0}\pi {R^2}} \over {\pi {R^2}{P_0} + Mg}}} \right)(2L)$$
B
$$\left( {{{{P_0}\pi {R^2} - Mg} \over {\pi {R^2}{P_0}}}} \right)(2L)$$
C
$$\left( {{{{P_0}\pi {R^2} + Mg} \over {\pi {R^2}{P_0}}}} \right)(2L)$$
D
$$\left( {{{{P_0}\pi {R^2}} \over {\pi {R^2}{P_0} - Mg}}} \right)(2L)$$

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