1
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
A particle moves such that its position vector $$\overrightarrow r \left( t \right) = \cos \omega t\widehat i + \sin \omega t\widehat j$$ where $$\omega$$ is a constant and t is time. Then which of the following statements is true for the velocity $$\overrightarrow v \left( t \right)$$ and acceleration $$\overrightarrow a \left( t \right)$$ of the particle :
A
$$\overrightarrow v$$ and $$\overrightarrow a$$ both are perpendicular to $$\overrightarrow r$$
B
$$\overrightarrow v$$ and $$\overrightarrow a$$ both are parallel to $$\overrightarrow r$$
C
$$\overrightarrow v$$ is perpendicular to $$\overrightarrow r$$ and $$\overrightarrow a$$ is directed towards the origin
D
$$\overrightarrow v$$ is perpendicular to $$\overrightarrow r$$ and $$\overrightarrow a$$ is directed away from the origin
2
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
A particle is moving with speed v = b$$\sqrt x$$ along positive x-axis. Calculate the speed of the particle at time t = $$\tau$$(assume that the particle is at origin t = 0)
A
$${{{b^2}\tau } \over {\sqrt 2 }}$$
B
$${{b^2}\tau }$$
C
$${{{b^2}\tau } \over 2}$$
D
$${{{b^2}\tau } \over 4}$$
3
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h1 and h2. Which of the following is correct ?
A
R2 = h1h2
B
R2 = 16 h1h2
C
R2 = 4 h1h2
D
R2 = 2h1h2
4
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1t2 is -
A
$${{2R} \over g}$$
B
$${R \over g}$$
C
$${R \over {2g}}$$
D
$${R \over {4g}}$$
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