Motion in a Straight Line Set-1 MCQ Online Practice Test | Class JEE

Q1. A ball is released from a height $h$ . If $t_1$ and $t_2$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_1$ and $t_2$ . [(JEE Main 2022)]

(A)

$t_1 = (\sqrt{2}) t_2$

(B)

$t_1 = (\sqrt{2} - 1) t_2$

(C)

$t_2 = (\sqrt{2} + 1) t_1$

(D)

$t_2 = (\sqrt{2} - 1) t_1$

Q2. A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws $n$ balls per second, the maximum height the balls can reach is [(JEE Main 2022)]

(A)

$g / 2 n$

(B)

$g / n$

(C)

$2 g n$

(D)

$g / 2 n^2$

Q3. A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height $h$ . Find the ratio of the times in which it is at height $h / 3$ while going up and coming down respectively. [(JEE Main 2022)]

(A)

$\frac{1}{\sqrt{3}}$

(B)

$\frac{\sqrt{2}}{\sqrt{3}}$

(C)

$\frac{\sqrt{3}}{\sqrt{2}}$

(D)

$1/3$

Q4. At time $t=0$ a particle starts travelling from a height $7 \ \mathrm{m}$ in a plane keeping $z$ coordinate constant. At any instant of time it's position along the $\hat{i}$ and $\hat{j}$ directions are defined as $3t$ and $5t^3$ respectively. At $t = 1 \ \mathrm{s}$ acceleration of the particle will be [(JEE Main 2022)]

(A)

$-30 \hat{j}$

(B)

$30 \hat{j}$

(C)

$3 \hat{i} + 15 \hat{j}$

(D)

$15 \hat{j}$

Q5. A NCC parade is going at a uniform speed of $9 \ \mathrm{km/h}$ under a mango tree on which a monkey is sitting at a height of $19.6 \ \mathrm{m}$ . At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: (Given $g=9.8 \ \mathrm{m/s}^2$ ) [(JEE Main 2022)]

(A)

5 m

(B)

10 m

(C)

19.8 m

(D)

24.5 m

Q6. A bullet is shot vertically downwards with an initial velocity of $100 \ \mathrm{m/s}$ from a certain height. Within $10 \ \mathrm{s}$ , the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time $t = 20 \ \mathrm{s}$ will be: (Take $g = 10 \ \mathrm{m/s}^2$ ) [(JEE Main 2022)]

(A)

Graph (a)

(B)

Graph (b)

(C)

Graph (c)

(D)

Graph (d)

Q7. Two projectiles are thrown with same initial velocity making an angle of $45^\circ$ and $30^\circ$ with the horizontal respectively. The ratio of their respective ranges will be : [(JEE Main 2022)]

(A)

$1 : \sqrt{2}$

(B)

$\sqrt{2} : 1$

(C)

$2 : \sqrt{3}$

(D)

$\sqrt{3} : 2$

Q8. Two projectiles thrown at $30^\circ$ and $45^\circ$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is : [(JEE Main 2022)]

(A)

$1:2$

(B)

$2:1$

(C)

$\sqrt{3}:\sqrt{2}$

(D)

$\sqrt{2}:\sqrt{3}$

Q9. A ball is projected from the ground with a speed $15 \ \mathrm{ms}^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then ' $\tan \theta$ ' will be equal to : [(JEE Main 2022)]

(A)

$1 / 4$

(B)

$1 / 2$

(C)

2

(D)

4

Q10. Two projectiles $P_1$ and $P_2$ thrown with speed in the ratio $\sqrt{3} : \sqrt{2}$ , attain the same height during their motion. If $P_2$ is thrown at an angle of $60^\circ$ with the horizontal, the angle of projection of $P_1$ with horizontal will be : [(JEE Main 2022)]

(A)

$15^\circ$

(B)

$30^\circ$

(C)

$45^\circ$

(D)

$60^\circ$

Q11. A projectile is projected with velocity of $25 \ \mathrm{m/s}$ at an angle $\theta$ with the horizontal. After $t$ seconds its inclination with horizontal becomes zero. If $R$ represents horizontal range of the projectile, the value of $\theta$ will be : [use $g = 10 \ \mathrm{m/s}^2$ ] [(JEE Main 2022)]

(A)

$\frac{1}{2}$

(B)

$\frac{1}{3}$

(C)

$\frac{1}{4}$

(D)

$\frac{1}{5}$

Q12. Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by $X_P(t) = \alpha t + \beta t^2$ and $X_Q(t) = f t - t^2$ . At what time, both the buses have same velocity? [(JEE Main 2022)]

(A)

$\frac{f + \alpha}{\beta + 1}$

(B)

$\frac{f - \alpha}{2 (\beta + 1)}$

(C)

$\frac{\alpha + f}{2 (\beta - 1)}$

(D)

$\frac{f - \alpha}{2 (\beta + 1)}$

Q13. Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. [(JEE Main 2022)]
Assertion A : Two identical balls A and B thrown with same velocity ' $u$ ' at two different angles with horizontal attained the same range R. IF A and B reached the maximum height $h_1$ and $h_2$ respectively, then $R = 4 \sqrt{h_1 h_2}$ .
Reason R : Product of said heights $h_1 h_2 = \frac{R^2}{16}$ . Choose the correct answer :

(A)

Both A and R are true and R is the correct explanation of A.

(B)

Both A and R are true but R is NOT the correct explanation of A.

(C)

A is true but R is false.

(D)

A is false but R is true.

Q14. A girl standing on road holds her umbrella at $45^\circ$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2} \ \mathrm{kmh}^{-1}$ , the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is : [(JEE Main 2022)]

(A)

$30 \ \mathrm{kmh}^{-1}$

(B)

$25 \sqrt{2} \ \mathrm{kmh}^{-1}$

(C)

$30 \sqrt{2} \ \mathrm{kmh}^{-1}$

(D)

$25 \ \mathrm{kmh}^{-1}$

Q15. A projectile is launched at an angle ' $\alpha$ ' with the horizontal with a velocity $20 \ \mathrm{ms}^{-1}$ . After $10 \ \mathrm{s}$ , its inclination with horizontal is ' $\beta$ '. The value of $\tan \beta$ will be : ( $g = 10 \ \mathrm{ms}^{-2}$ ). [(JEE Main 2022)]

(A)

$\tan \alpha + 5 \sec \alpha$

(B)

$\tan \alpha - 5 \sec \alpha$

(C)

$2 \tan \alpha - 5 \sec \alpha$

(D)

$2 \tan \alpha + 5 \sec \alpha$

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