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Kinematics-2D

257 Questions Start Errorless Test
All Exams Allen Objective Errorless
NEET 2024 Q1 Errorless 5. Critical Thinking MCQ
A particle moving with uniform speed in a circular path maintains
A.
Constant velocity
B.
Constant acceleration
C.
Constant velocity but varying acceleration
D.
Varying velocity and varying acceleration
NEET 2024 Q2 Errorless 5. Critical Thinking MCQ
A bob is whirled in a horizontal plane by means of a string with an initial speed of $\omega$ rpm. The tension in the string is T. If speed becomes $2\omega$ while keeping the same radius, the tension in the string becomes
A.
$T$
B.
$4T$
C.
$\frac{T}{4}$
D.
$\sqrt{2} T$
JEE (Main) 2023 Q3 Errorless 5. Critical Thinking MCQ
The maximum vertical height to which a man can throw a ball is $136m$ . The maximum horizontal distance upto which he can throw the same ball is
A.
$192m$
B.
$136m$
C.
$272m$
D.
$68m$
JEE (Main) 2023 Q4 Errorless 5. Critical Thinking MCQ
A stone is projected at angle $30^{\circ}$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be
A.
1:2
B.
1:4
C.
4:1
D.
4:3
JEE (Main) 2023 Q5 Errorless 5. Critical Thinking MCQ
The initial speed of a projectile fired form ground is u. At the highest point during its motion, the speed of projectile $\frac{\sqrt{3}}{2}u$ . The time of flight of the projectile is
A.
$\frac{u}{2g}$
B.
$\frac{u}{g}$
C.
$\frac{2u}{g}$
D.
$\frac{\sqrt{3}u}{g}$
JEE (Main) 2023 Q6 Errorless 5. Critical Thinking MCQ
A body is moving with constant speed, in a circle of radius 10m. The body completes one revolution in 4s. At the end of 3rd second, the displacement of body (in m) from its starting point is
A.
30
B.
$15\pi$
C.
$5\pi$
D.
$10\sqrt{2}$
JEE (Main) 2023 Q7 Errorless 5. Critical Thinking MCQ
For a body projected at an angle with the horizontal from the ground, choose the correct statement
A.
Gravitational potential energy is maximum at the highest point.
B.
The horizontal component of velocity is zero at highest point
C.
The vertical component of momentum is maximum at the highest point
D.
The kinetic energy (K.E.) is zero at the highest point of projectile motion
JEE (Main) 2023 Q8 Errorless 5. Critical Thinking MCQ
A car is moving with a constant speed of 20m/s in a circular horizontal track of radius 40m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be (Take g = 10m/s $^{2}$ )
A.
$\frac{\pi}{6}$
B.
$\frac{\pi}{2}$
C.
$\frac{\pi}{4}$
D.
$\frac{\pi}{3}$
JEE (Main) 2022 Q9 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) 2022 Q10 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) 2022 Q11 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.
42 m
B.
47m
C.
19 m
D.
40m
JEE (Main) 2022 Q12 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) 2022 Q13 Errorless 5. Critical Thinking MCQ
A ball is projected from the ground with a speed $15 \, ms^{-1}$ 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) 2022 Q14 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) 2022 Q15 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) 2022 Q16 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) 2022 Q17 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.
$-\frac{v^{2}}{R}\hat{i}+\frac{v^{2}}{R}\hat{j}$
NEET 2022 Q18 Errorless 5. Critical Thinking MCQ
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.
$5 \, ms^{-1}$
B.
$10 \, ms^{-1}$
C.
Zero
D.
$5\sqrt{3} \, ms^{-1}$
JEE (Main) 2021 Q19 Errorless 5. Critical Thinking MCQ
An electron with kinetic energy $K_{1}$ enters between parallel plates of a capacitor at an angle ' $\alpha'$ with the plates. It leaves the plates at angle ' $\beta'$ with kinetic energy $K_{2}$ . Then the ratio of kinetic energies $K_{1}:K_{2}$ will be
A.
$\frac{\sin^{2}\beta}{\cos^{2}\alpha}$
B.
$\frac{\cos^{2}\beta}{\cos^{2}\alpha}$
C.
$\frac{\cos\beta}{\cos\alpha}$
D.
$\frac{\cos\beta}{\sin\alpha}$
JEE (Main) 2021 Q20 Errorless 5. Critical Thinking MCQ
The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta x^{2}$ , where $\alpha$ and $\beta$ are constants and x and y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained H are respectively given by
A.
$\tan^{-1}\alpha,\frac{\alpha^{2}}{4\beta}$
B.
$\tan^{-1}\beta,\frac{\alpha^{2}}{2\beta}$
C.
$\tan^{-1}\beta,\frac{4\alpha^{2}}{\beta}$
D.
$\tan^{-1}\left(\frac{\beta}{\alpha}\right),\frac{\alpha^{2}}{\beta}$
JEE (Main) 2021 Q21 Errorless 5. Critical Thinking MCQ
Statement-I : A cyclist is moving on an unbanked road with a speed of $7kmh^{-1}$ and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve ( $g = 9.8m/s^{2}$ ). Statement-II : If the road is banked at an angle of $45^{\circ}$ , cyclist can cross the curve of 2m radius with the speed of $18.5 kmh^{-1}$ without slipping. In the light of the above statements, choose the correct answer from the option 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) 2021 Q22 Errorless 5. Critical Thinking MCQ
A modern grand-prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is $\mu_{s}$ , then the magnitude of negative lift $F_{L}$ acting downwards on the car is (Assume forces on the four tyres are identical and g = acceleration due to gravity)
A.
$m\left(\frac{v^{2}}{\mu_{s}R}+g\right)$
B.
$m\left(\frac{v^{2}}{\mu_{s}R}-g\right)$
C.
$m\left(g-\frac{v^{2}}{\mu_{s}R}\right)$
D.
$-m\left(g+\frac{v^{2}}{\mu_{s}R}\right)$
JEE (Main) 2021 Q23 Errorless 5. Critical Thinking MCQ
A particle of mass m moves in a circular orbit under the central potential field, $U(r) = \frac{-C}{r}$ , where C is a positive constant. The correct radiusā€“velocity graph of the particle's motion is
A.
B.
C.
D.
JEE (Main) 2021 Q24 Errorless 5. Critical Thinking MCQ
A butterfly is flying with a velocity $4\sqrt{2}$ m/s in North-East direction. Wind is slowly blowing at 1m/s from North to South. The resultant displacement of the butterfly in 3 seconds is
A.
3 m
B.
20 m
C.
$12\sqrt{2}$ m
D.
15 m
JEE (Main) 2021 Q25 Errorless 5. Critical Thinking MCQ
The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are $R_{1}, R_{2}$ and $H_{1}, H_{2}$ respectively. Choose the correct option
A.
$R_{1} > R_{2}$ and $H_{1} = H_{2}$
B.
$R_{1} = R_{2}$ and $H_{1} < H_{2}$
C.
$R_{1} < R_{2}$ and $H_{1} < H_{2}$
D.
$R_{1} = R_{2}$ and $H_{1} = H_{2}$