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Motion in a Lane MCQs for NEET — Physics Questions with Answers

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A particle is projected at an angle $θ$ with horizontal with an initital speed u. When it makes and angle $α$ with horizontal, its speed is

$u \cos θ$

$u \cos θ u \cos α$

$\frac{u \sin θ}{\sin α}$

$\frac{u \cos θ}{\cos α}$

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Explanation

Horizontal component of velocity remains constant during projectile motion

so,

$v \cos α = u \cos θ \Rightarrow v = \frac{u \cos θ}{\cos α}$

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A body is projected with velocity $20 \sqrt{3}$ m/s with an angle of projection 60 $°$ with horizontal. Calculate velocity on that point where body makes an angle 30 $°$ with the horizontal.

20 m/s

$\frac{20}{\sqrt{3}} m / s$

$10 \sqrt{3} m / s$

10 m/s

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Explanation

Horizontal velocity is always constant during projectile motion, when only gravitational force act on the body.

So, $v \cos α = u \cos θ$

$v \times \frac{\sqrt{3}}{2} = 20 \sqrt{3} \times \frac{1}{2} \Rightarrow v = 20 m / s$

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A particle is projected with a velocity u making an angle $θ$ with the horizontal. At any instant, its velocity V is at right angles to its initial velocity u; then V is:

u cos $θ$

u tan $θ$

u cot $θ$

u sec $θ$

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A projectile is given an initial velocity of $\hat{i} + 2 \hat{j}$ . The cartesian equation of its path is (g = 10 ${ms}^{- 2}$ )

$y = 2 x - 5 x^{2}$

$y = x - 5 x^{2}$

$4 y = 2 x - 5 x^{2}$

$y = 2 x - 25 x^{2}$

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Explanation

$y = x \tan θ - \frac{g x^{2}}{2 u^{2} \cos^{2} θ} \{\begin{cases} u \cos θ = 1 \\ u \sin θ = 2 \end{cases} y = 2 x - \frac{10 x^{2}}{2 \times 1} = 2 x - 5 x^{2}$

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A particle projected with kinetic energy $k_{0}$ with an angle of projection $θ$ . Then the variation of kinetic K with vertical displacement y is

linear

parabolic

hyperbolic

periodic

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A body is thrown horizontally with a velocity $\sqrt{2 g h}$ from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is:

$\frac{h}{2}$

$\frac{2 h}{3}$

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Explanation

$x = u \sqrt{\frac{2 h}{g}} = \sqrt{2 g h} \sqrt{\frac{2 h}{g}} x = 2 h$

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A particle starts from the origin at t=0 and moves in the x-y plane with constant acceleration 'a' in the y direction. Its equation of motion is $y = b x^{2}$ . The x component of its velocity (at t=0) is:

variable

$\sqrt{\frac{2 a}{b}}$

$\frac{a}{2 b}$

$\sqrt{\frac{a}{2 b}}$

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Explanation

$y = b x^{2} \frac{d y}{d t} = 2 b x \frac{d x}{d t} \Rightarrow \frac{d^{2} y}{d t^{2}} = 2 b [{(\frac{d x}{d t})}^{2}] \sqrt{\frac{a}{2 b}} = v_{x}$

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A body projected with velocity u with an angle of projection $θ$ . Change in velocity after the time (t) from the projection is:

$\frac{1}{2} g t^{2}$

u sin $θ$

u cos $θ$

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Explanation

$\vec{u} = u \cos θ \hat{i} + u \sin θ \hat{j} A f t e r t i m e t : \vec{v} = u \cos θ \hat{i} + (u \sin θ - g t) \hat{j} C h a n g e i n v e l o c i t y, ∆ \vec{v} = \vec{v} - \vec{u} = u \cos θ \hat{i} + (u \sin θ - g t) \hat{j} - (u \cos θ \hat{i} + u \sin θ \hat{j}) \Rightarrow ∆ \vec{v} = (- g t) \hat{j} \Rightarrow |∆ \vec{v}| = (g t)$

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A particle has initial velocity $(3 \hat{i} + 4 \hat{j})$ and has acceleration $(0.4 \hat{i} + 0.3 \hat{j})$ . Its speed after 10 s

7 units

$7 \sqrt{2}$ units

8.5 units

10 units

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Explanation

$\vec{v} = \vec{u} + \vec{a} t = (3 \hat{i} + 4 \hat{j}) + (0.4 \hat{i} + 0.3 \hat{j}) \times 10 = 7 \hat{i} + 7 \hat{j} | \vec{v} | = \sqrt{7^{2} + 7^{2}} = 7 \sqrt{2} m / s$

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The gravity in space is given by $\vec{g} = - 10 \hat{j} m s^{- 2}$ . Two particles are simultaneously projected with velocity $\vec{u_{1}} = (10 m s^{- 1}) \hat{i} + (10 m s^{- 1}) \hat{j}$ and $\vec{u_{2}} = (20 m s^{- 1}) \hat{i} + (10 m s^{- 1}) \hat{j}$ . Then, the ratio of their times of flight

1:1

1:2

2:1

none

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Explanation

$T i m e o f f l i g h t = \frac{2 u_{y}}{g} \frac{T_{1}}{T_{2}} = \frac{u_{y, 1}}{u_{y, 2}} = \frac{10}{10} = 1$

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