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Motion in a Plane
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A particle moving with uniform speed in a circular path maintains;A constant velocity but varying acceleration.B varying velocity and varying acceleration.C constant velocity.D constant acceleration.
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A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is:A along south-westB along eastwardC along northwardD along north-east
Change in velocity points north-east, so the force is along north-east.
Initial velocity $=-v\hat{j}$, final velocity $=v\hat{i}$ Change in velocity $=v\hat{i}-(-v\hat{j})=v(\hat{i}+\hat{j})$ Momentum gain is along $\hat{i}+\hat{j}$ $\Rightarrow$ force experienced is along $\hat{i}+\hat{j}$ $\Rightarrow$ force experienced is in North-East direction. -
A bullet is fired from a gun at the speed of $280\ m/s$ in the direction $30^\circ$ above the horizontal. The maximum height attained by the bullet is ($g=9.8\ ms^{-2}$, $\sin30^\circ=0.5$)A 3000 mB 2800 mC 2000 mD 1000 m
$h_{max}=\frac{u^2\sin^2\theta}{2g}=1000\ m$.
$h_{max}=\frac{u^2\sin^2\theta}{2g}=\frac{280\times280}{2\times9.8}\times\frac{1}{4}=1000\ m$ -
A ball is projected with a velocity, $10\ ms^{-1}$, at an angle of $60^\circ$ with the vertical direction. Its speed at the highest point of its trajectory will be :A $10\ ms^{-1}$B ZeroC $5\sqrt{3}\ ms^{-1}$D $5\ ms^{-1}$
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A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it equals $4R$. The angle of projection, $\theta$, is then given by:A $\theta=\cos^{-1}\left(\frac{\pi^2R}{gT^2}\right)^{1/2}$B $\theta=\sin^{-1}\left(\frac{\pi^2R}{gT^2}\right)^{1/2}$C $\theta=\sin^{-1}\left(\frac{2gT^2}{\pi^2R}\right)^{1/2}$D $\theta=\cos^{-1}\left(\frac{gT^2}{\pi^2R}\right)^{1/2}$
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A car starts from rest and accelerates at $5\ m/s^2$. At $t=4$ s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t=6$ s?A $20\ m/s,\ 0$B $20\sqrt{2}\ m/s,\ 0$C $20\sqrt{2}\ m/s,\ 10\ m/s^2$D $20\ m/s,\ 5\ m/s^2$
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The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by:A $30^\circ$ westB $0^\circ$C $60^\circ$ westD $45^\circ$ west
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Two particles A and B are moving in uniform circular motion in concentric circles of radius $r_A$ and $r_B$ with speed $v_A$ and $v_B$ respectively. The time period of rotation is the same. The ratio of angular speed of A to that of B will be:A $r_A:r_B$B $v_A:v_B$C $r_B:r_A$D $1:1$