Physics - Motion Plane - Quiz-11

Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)

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The faster one
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The slower one
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Depends on masses
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Both will reach simultaneously

A pilot is supposed to fly east from A to B and back again A due west. If the wind is blowing due south, find time for the round trip, if AB = l. The velocity of the plane in the air is v and the velocity of wind is u.

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$\frac{l}{\sqrt{v^{2} + u^{2}}}$
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$\frac{2 l}{\sqrt{v^{2} - u^{2}}}$
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$\frac{l}{\sqrt{v^{2} - u^{2}}}$
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$\frac{l}{v + u}$

A spotlight (source) is fixed 4 m from the vertical wall and is rotating at rate 1 rad/s. The spot (image) moves horizontally on the wall. The speed of the spot on the wall, when the spotlight makes the angle of 45° with the wall, is (The line joining spot source and image is in the horizontal plane)

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2 m/s
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3 m/s
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8 m/s
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1 m/s

A projectile is projected from the ground such that 2 seconds before it reaches the highest point, its initial velocity makes an angle of 37° with vertical. Then the velocity of the projectile at the highest point is:

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5 m/s
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10 m/s
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15 m/s
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20 m/s

A ball is projected horizontally from the top of wall A of height 80 m with speed 10 m/s. At what distance from the wall ball hits the ground?

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20 m
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50 m
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(3) 60 m
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40 m

A swimmer swims a distance d upstream in 4 s and swims an equal distance downstream in 2 s. The ratio of swimmer's speed in still water to the speed of river water will be:

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$\frac{6}{5}$
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$\frac{3}{1}$
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$\frac{5}{3}$
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$\frac{4}{3}$

A particle starts from (-1, 0) in the x-y plane along a straight path making an angle of 60° with the X-axis. Which of the following will not be the coordinate through which the particle will pass?

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(0, $\sqrt{3}$ )
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(1, 2 $\sqrt{3}$ )
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(2, 3 $\sqrt{3}$ )
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(4, 4 $\sqrt{3}$ )

An aeroplane flies 400 m north and then 300 m west and then flies 1200 m upwards. Its net displacement is

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1200 m
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1300 m
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1400 m
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1500 m

A projectile is thrown with an initial velocity ( $v_{x} \hat{i} + v_{y} \hat{j}$ )m/s. Consider horizontal direction and vertical direction as x and y axes respectively. If the range of the projectile is double the maximum height, then $\frac{v_{y}}{v_{x}}$ is

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4
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3
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2
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1

A car is moving on a circular track at a speed of 20 m/s having a radius of 100 m. If it starts decelerating uniformly at the rate of $3 m / s^{2}$ , the angle made by the resultant acceleration with the direction of its instantaneous velocity is:

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37°
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127°
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53°
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143°

A swimmer can swim in still water at a speed of 5 m/s and takes $t_{1} and t_{2}$ , time to cross a river in the shortest time and shortest path respectively. If the speed of the river increases, the time is taken to cross the river in the shortest time and the shortest path be $t'_{1} and t'_{2}$ respectively. Then

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$t_{1} < t_{1}^{'}, t_{2} < t_{2}^{'}$
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$t_{1} > t_{1}^{'}, t_{2} > t_{2}^{'}$
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$t_{1} = t_{1}^{'}, t_{2} < t_{2}^{'}$
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$t_{1} = t_{1}^{'}, t_{2} > t_{2}^{'}$

A sprinkler is deployed to irrigate the garden. The speed of water-jet from the sprinkler is u. The maximum area which can be irrigated by the sprinkler is

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$\frac{π^{2} u^{2}}{g}$
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$\frac{{πu}^{2}}{g}$
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$\frac{{πu}^{2}}{g^{2}}$
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$\frac{{πu}^{4}}{g^{2}}$

Which of the following is an appropriate expression for the radius of curvature of a projectile at the highest point? (R $\to$ Range of projectile)

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$\frac{R}{2} \cot θ$
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$\frac{R}{2} \tan θ$
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2R cot $θ$
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2R tan $θ$

The coordinates of a particle moving in the x-y plane vary with time according to the following relation:

$x = \frac{B}{t}$ , $y = A \sqrt{t}$ .

The locus of the particle is:

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Circle
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Eclipse
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Parabola
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Hyperbola

If $t_{1}$ represents the instant at which the instantaneous velocity becomes perpendicular to the direction of initial velocity during a projectile and $t_{2}$ represents the time after which the particle attains maximum height, then $\sqrt{t_{1} t_{2}}$ is:

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$\frac{u}{g}$
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$\frac{2 u}{g}$
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$\frac{u}{2 g}$
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$\frac{u \sin^{2} θ}{g}$

A park is in the shape of a regular hexagon. Six friends standing at each corner of the park start moving towards each other with the same speed 2 m/s and meet each other after 60 s. The side of the park is

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120 m
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30 m
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240 m
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60 m

A ball is projected horizontally from a cliff 40 m high at a speed of 40 m/s and simultaneously a ball is dropped. If the time taken by the two balls to reach the ground are $t_{1} and t_{2}$ respectively (taking air friction into consideration), then

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$t_{1} > t_{2}$
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$t_{1} < t_{2}$
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$t_{1} = t_{2}$
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Depending on air friction $t_{1}$ maybe less or more than $t_{2}$

Select the incorrect statement.

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It is possible to have $|\frac{d \vec{v}}{dt}| = 0$ and $\frac{d |\vec{v}|}{dt} \neq 0$ .
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It is possible to have $|\frac{d \vec{v}}{dt}| \neq 0$ and $\frac{d |\vec{v}|}{dt} = 0$ .
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it is possible to have $|\frac{d \vec{v}}{dt}| = 0$ and $\frac{d |\vec{v}|}{dt} = 0$ .
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It is possible to have $|\frac{d \vec{v}}{dt}| \neq 0$ and $\frac{d |\vec{v}|}{dt} \neq 0$ .

A projectile is fired horizontally from the top of a tower. The time after which the instantaneous velocity will be perpendicular to the initial velocity is (neglect air resistance) :

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$t = \frac{u \sin θ}{g}$
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$t = \frac{u}{g \sin θ}$
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$t = \frac{u}{g \cos θ}$
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It will never be perpendicular at any instant

A particle of mass 2 kg is moving in a circular path with a constant speed of 10 m/s. The change in the magnitude of velocity when a particle travels from P to Q will be (assume the radius of the circle is 10/ $π^{2}$ ]