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Kinematics-2D

212 Questions Start Errorless Test
All Exams Allen Advance Errorless
JEE (Main) April 2023 Q26 Errorless 5. Critical Thinking MCQ
A projectile is projected at $30^{\circ}$ from horizontal with initial velocity $40ms^{-1}$ . The velocity of the projectile at t=2s from the start will be (Given $g=10m/s^{2}$ )
A.
$20\sqrt{3}ms^{-1}$
B.
$40\sqrt{3}ms^{-1}$
C.
$20ms^{-1}$
D.
Zero
JEE (Main) April 2023 Q27 Errorless 5. Critical Thinking MCQ
A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ}$ , the ratio of instantaneous velocity to its average velocity is $\pi: x\sqrt{2}$ . The value of x will be
A.
2
B.
5
C.
1
D.
7
JEE (Main) April 2023 Q28 Errorless 5. Critical Thinking MCQ
Two projectiles A and B are thrown with initial velocities of 40 m/s and 60 m/s at angles $30^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The ratio of their ranges respectively is $(g = 10\,m/s^{2})$
A.
$\sqrt{3}:2$
B.
$2:\sqrt{3}$
C.
1:1
D.
4:9
JEE (Main) April 2023 Q29 Errorless 5. Critical Thinking MCQ
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: When a body is projected at an angle $45^{\circ}$ , it's range is maximum. Reason R: For maximum range, the value of $\sin2\theta$ should be equal to one. In the light of the above statements, choose the correct answer from the options given below
A.
If both assertion and reason are true and the reason is the correct explanation of the assertion.
B.
If both assertion and reason are true but reason is not the correct explanation of the assertion.
C.
If assertion is true but reason is false.
D.
If the assertion and reason both are false.
E.
If assertion is false but reason is true.
JEE (Main) April 2023 Q30 Errorless 5. Critical Thinking MCQ
As shown in the figure, a particle is moving with constant speed $\pi m / s$ . Considering its motion from $A$ to $B$ , the magnitude of the average velocity is
A.
$\pi m / s$
B.
$\sqrt{3} m / s$
C.
$2\sqrt{3} m / s$
D.
$1.5\sqrt{3} m / s$
JEE (Main) April 2023 Q31 Errorless 5. Critical Thinking MCQ
A child of mass 5 kg is going round a merry-go-round that makes 1 rotation in 3.14 s. The radius of the merry-go-round is 2 m. The centrifugal force on the child will be
A.
80 N
B.
50 N
C.
100 N
D.
40 N
JEE (Main) April 2023 Q32 Errorless 5. Critical Thinking MCQ
For particle P revolving round the centre O with radius of circular path r and angular velocity $\omega$ , as shown in below figure, the projection of OP on the x-axis at time t is
A.
$x(t) = r\cos \left(\omega t + \frac{\pi}{6}\right)$
B.
$x(t) = r\cos (\omega t)$
C.
$x(t) = r\sin \left(\omega t + \frac{\pi}{6}\right)$
D.
$x(t) = r\cos \left(\omega t - \frac{\pi}{6}\omega\right)$
JEE (Main) April 2023 Q33 Errorless 5. Critical Thinking MCQ
The trajectory of projectile, projected from the ground is given by $y = x - \frac{x^{2}}{20}$ . Where x and y are measured in meter. The maximum height attained by the projectile will be
A.
5 m
B.
$10\sqrt{2}$ m
C.
200 m
D.
10 m
JEE (Main) April 2023 Q34 Errorless 5. Critical Thinking MCQ
The range of the projectile projected at an angle of $15^{\circ}$ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of $45^{\circ}$ with horizontal, then its range will be
A.
50 m
B.
$50\sqrt{2}$ m
C.
100 m
D.
$100\sqrt{2}$ m
JEE (Main) June 2022 Q35 Errorless 5. Critical Thinking MCQ
A projectile is projected with velocity of 25 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 $g = 10 \, m/s^{2}$ ]
A.
$\frac{1}{2} \sin^{-1} \left( \frac{5t^{2}}{4R} \right)$
B.
$\frac{1}{2} \sin^{-1} \left( \frac{4R}{5t^{2}} \right)$
C.
$\tan^{-1} \left( \frac{4t^{2}}{5R} \right)$
D.
$\cot^{-1} \left( \frac{R}{20t^{2}} \right)$
JEE (Main) June 2022 Q36 Errorless 5. Critical Thinking MCQ
A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $\sqrt{x(u^{2}-gL)}$ . The value of x is
A.
3
B.
2
C.
1
D.
5
JEE (Main) June 2022 Q37 Errorless 5. Critical Thinking MCQ
A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is
A.
The same throughout the motion
B.
Minimum at the highest position of the circular path
C.
Minimum at the lowest position of the circular path
D.
Minimum when the rope is in the horizontal position
JEE (Main) June 2022 Q38 Errorless 5. Critical Thinking MCQ
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R Assertion A : Two identical balls A and B thrown with same velocity ā€˜uā€™ 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 $h_{1}h_{2}=\left(\frac{u^{2}\sin^{2}\theta}{2g}\right)\cdot\left(\frac{u^{2}\cos^{2}\theta}{2g}\right)$ Choose the CORRECT answer
A.
If both assertion and reason are true and the reason is the correct explanation of the assertion.
B.
If both assertion and reason are true but reason is not the correct explanation of the assertion.
C.
If assertion is true but reason is false.
D.
If the assertion and reason both are false.
JEE (Main) June 2022 Q39 Errorless 5. Critical Thinking MCQ
A person can throw a ball up to a maximum range of 100 m. How high above the ground he can throw the same ball
A.
25 m
B.
50 m
C.
100 m
D.
200 m
JEE (Main) June 2022 Q40 Errorless 5. Critical Thinking MCQ
For a particle in uniform circular motion, the acceleration $\vec{a}$ at any point $P(R,\theta)$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive $x$ -axis and $v$ is uniform speed)
A.
$-\frac{v^2}{R}\sin \theta \hat{i} +\frac{v^2}{R}\cos \theta \hat{j}$
B.
$-\frac{v^2}{R}\cos \theta \hat{i} +\frac{v^2}{R}\sin \theta \hat{j}$
C.
$-\frac{v^2}{R}\cos \theta \hat{i} -\frac{v^2}{R}\sin \theta \hat{j}$
D.
$-\frac{v^2}{R}\hat{i} +\frac{v^2}{R}\hat{j}$
JEE (Main) June 2022 Q41 Errorless 5. Critical Thinking MCQ
A projectile is launched at an angle ' $\alpha'$ with the horizontal with a velocity $20ms^{-1}$ . After 10 s, its inclination with horizontal is ' $\beta'$ . The value of tan $\beta$ will be ( $g = 10ms^{-2}$ )
A.
$\tan\alpha+5\sec\alpha$
B.
$\tan\alpha-5\sec\alpha$
C.
$2\tan\alpha-5\sec\alpha$
D.
$2\tan\alpha+5\sec\alpha$
JEE (Main) June 2022 Q42 Errorless 5. Critical Thinking MCQ
Motion of a particle in $x - y$ plane is described by a set of following equations $x = 4\sin \left(\frac{\pi}{2} -\omega t\right)m$ and $y = 4\sin (\omega t)m$ The path of particle will be
A.
Circular
B.
Helical
C.
Parabolic
D.
Elliptical
JEE (Main) June 2022 Q43 Errorless 5. Critical Thinking MCQ
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 $15\sqrt{2}kmh^{-1}$ , the rain drops hit her head vertically. The speed of rain drops with respect to the moving girls is
A.
$30 kmh^{-1}$
B.
$\frac{25}{\sqrt{2}} kmh^{-1}$
C.
$\frac{30}{\sqrt{2}} kmh^{-1}$
D.
$25 kmh^{-1}$
JEE (Main) June 2022 Q44 Errorless 5. Critical Thinking MCQ
The distance of the Sun from Earth is $1.5 \times 10^{11} m$ and its angular diameter is (2000) s when observed from the Earth. The diameter of the Sun will be
A.
$2.45 \times 10^{10} m$
B.
$1.45 \times 10^{10} m$
C.
$1.45 \times 10^{9} m$
D.
$0.14 \times 10^{9} m$
JEE (Main) July 2022 Q45 Errorless 5. Critical Thinking MCQ
A person moved from $A$ to $B$ on a circular path as shown in figure. If the distance travelled by him is $60~m$ , then the magnitude of displacement would be (Given $\cos 135^{\circ} = -0.7$ )
A.
42m
B.
47m
C.
19m
D.
40m
JEE (Main) July 2022 Q46 Errorless 5. Critical Thinking MCQ
A ball is projected with kinetic energy $E$ , at an angle of $60^{\circ}$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become
A.
Zero
B.
$\frac{E}{2}$
C.
$\frac{E}{4}$
D.
$E$
JEE (Main) July 2022 Q47 Errorless 5. Critical Thinking MCQ
A ball is projected from the ground with a speed $15ms^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then 'tan $\theta'$ will be equal to
A.
$\frac{1}{4}$
B.
$\frac{1}{2}$
C.
2
D.
4
JEE (Main) July 2022 Q48 Errorless 5. Critical Thinking MCQ
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
A.
$1:\sqrt{2}$
B.
$\sqrt{2}:1$
C.
$2:\sqrt{3}$
D.
$\sqrt{3}:2$
JEE (Main) July 2022 Q49 Errorless 5. Critical Thinking MCQ
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
A.
$1:\sqrt{2}$
B.
2:1
C.
$\sqrt{2}:1$
D.
1:2
JEE (Main) July 2022 Q50 Errorless 5. Critical Thinking MCQ
A body of mass 10 kg is projected at an angle of $45^{\circ}$ with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time $t = \frac{T}{\sqrt{2}}$ , is ____ [Take $g = 10 m / s^{2}$ ]
A.
$100\hat{i} + (100\sqrt{2} - 200)\hat{j}$
B.
$100\sqrt{2}\hat{i} + (100 - 200\sqrt{2})\hat{j}$
C.
$100\hat{i} + (100 - 200\sqrt{2})\hat{j}$
D.
$100\sqrt{2}\hat{i} + (100\sqrt{2} - 200)\hat{j}$