Kinematics · JEE Main previous year questions

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2. B.
3. C.
4. D.

A ball of mass $4\mathrm{kg}$, moving with a velocity of $10\mathrm{m}{\mathrm{s}}^{-1}$, collides with a spring of length $8\mathrm{m}$ and force constant $100\mathrm{N}{\mathrm{m}}^{-1}$. The length of the compressed spring is x m. The value of x, to the nearest integer, is ____.

1. A.
2. B.
3. C.
4. D.

A boy pushes a box of mass 2 kg with a force $\vec{F}=\left(20\hat{i}+10\hat{j}\right)\mathrm{N}$ on a frictionless surface. If the box was initially at rest, then _________ m is displacement along the x-axis after 10s.

The trajectory of a projectile in a vertical plane is $y=\alpha x-\beta x^2$, where $\alpha$ and $\beta$ are constants and x & 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 :

1. A.${\tan }^{-1}\alpha ,\frac{{\alpha }^2}{4\beta }$
2. B.${\tan }^{-1}\alpha ,\frac{4{\alpha }^2}{\beta }$
3. C.${\tan }^{-1}\left(\frac{\beta }{\alpha }\right),\frac{{\alpha }^2}{\beta }$
4. D.${\tan }^{-1}\beta ,\frac{{\alpha }^2}{2\beta }$

A particle executes S.H.M., the graph of velocity as a function of displacement is :

1. A.a parabola
2. B.a helix
3. C.an ellipse
4. D.a circle

A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is $\frac{\sqrt{x}a}{2}$. The value of x is _________.

$Y=A\sin (\omega t+{\varphi }_0)$ is the time-displacement equation of a SHM. At $t=0$ the displacement of the particle is $Y=\frac{A}{2}$ and it is moving along negative x-direction. Then the initial phase angle ${\varphi }_0$ will be:

1. A.$\frac{5\pi }{6}$
2. B.$\frac{\pi }{3}$
3. C.$\frac{2\pi }{3}$
4. D.$\frac{\pi }{6}$

Particle A of mass $m_1$ moving with velocity $(\sqrt{3}\hat{i}+\hat{j})\mathrm{m}{\mathrm{s}}^{-1}$ collides with another particle B of mass $m_2$ which is at rest initially. Let ${\vec{V}}_1$ and ${\vec{V}}_2$ be the velocities of particles A and B after collision respectively. If $m_1=2m_2$ and after collision ${\vec{V}}_1=(\hat{i}+\sqrt{3}\hat{j})$, the angle between ${\vec{V}}_1$ and ${\vec{V}}_2$ is :

1. A.$105^{\circ }$
2. B.$15^{\circ }$
3. C.$-45^{\circ }$
4. D.$60^{\circ }$

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle $60^{\circ }$ from the horizontal. On further increasing the speed of the car to $(1+\beta )v$, this angle changes to $45^{\circ }$. The value of $\beta$ is close to :

1. A.$0.50$
2. B.$0.73$
3. C.$0.37$
4. D.$0.41$

A Young's double-slit experiment is performed using monochromatic light of wavelength $\lambda$. The intensity of light at a point on the screen, where the path difference is $\lambda$, is K units. The intensity of light at a point where the path difference is $\frac{\lambda }{6}$ is given by $\frac{nK}{12}$, where n is an integer. The value of n is ______ .

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it reaches the top of the rope ?

1. A.12
2. B.3
3. C.9
4. D.6

A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force F on the ball and moves horizontally a distance of 0.2 m while launching the ball, the value of F (in N) is ($g=10\mathrm{m}{\mathrm{s}}^{-2}$) _______.

1. A.
2. B.
3. C.
4. D.

Two light waves having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first wave travels a path ${\mathrm{L}}_1$ through a medium of refractive index $n_1$ while the second wave travels a path of length ${\mathrm{L}}_2$ through a medium of refractive index $n_2$. After this the phase difference between the two waves is :

1. A.$\frac{2\pi }{\lambda }(n_1{L}_1-n_2{L}_2)$
2. B.$\frac{2\pi }{\lambda }(n_2{L}_1-n_1{L}_2)$
3. C.$\frac{2\pi }{\lambda }\left(\frac{L_1}{n_1}-\frac{L_2}{n_2}\right)$
4. D.$\frac{2\pi }{\lambda }\left(\frac{L_2}{n_1}-\frac{L_1}{n_2}\right)$

Train A and train B are running on parallel tracks in the opposite directions with speeds of 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/ hour. Speed (in ${\text{ms}}^{-1}$) of this person as observed from train B will be close to : (take the distance between the tracks as negligible)

1. A.$30.5{\text{ ms}}^{-1}$
2. B.$29.5{\text{ ms}}^{-1}$
3. C.$31.5{\text{ ms}}^{-1}$
4. D.$28.5{\text{ ms}}^{-1}$

1. A.(B), (C) and (D)
2. B.(A), (B) and (C)
3. C.(A) and (D)
4. D.(A), (B) and (D)

A particle of mass m is projected with a speed u from the ground at an angle $\theta =\frac{\pi }{3}$ w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $u\hat{i}$. The horizontal distance covered by the combined mass before reaching the ground is:

1. A.$2\sqrt{2}\frac{u^2}{g}$
2. B.$\frac{3\sqrt{3}}{8}\frac{u^2}{g}$
3. C.$\frac{3\sqrt{2}}{4}\frac{u^2}{g}$
4. D.$\frac{5}{8}\frac{u^2}{g}$

A particle moves such that its position vector $\vec{r}(t)=\cos \omega t\hat{i}+\sin \omega t\hat{j}$ where $\omega$ is a constant and t is time. Then which of the following statements is true for the velocity $\vec{v}(t)$ and acceleration $\vec{a}(t)$ of the particle :

1. A.$\vec{v}$ and $\vec{a}$ both are perpendicular to $\vec{r}$
2. B.$\vec{v}$ and $\vec{a}$ both are parallel to $\vec{r}$
3. C.$\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed towards the origin
4. D.$\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed away from the origin

The trajectory of a projectile near the surface of the earth is given as $y=2x-9x^2$. If it were launched at an angle ${\theta }_0$ with speed $v_0$ then ($g=10{\text{ ms}}^{-2}$) :

1. A.${\theta }_0={\cos }^{-1}\left(\frac{1}{\sqrt{5}}\right)$ and $v_0=\frac{5}{3}{\text{ ms}}^{-1}$
2. B.${\theta }_0={\cos }^{-1}\left(\frac{2}{\sqrt{5}}\right)$ and $v_0=\frac{3}{5}{\text{ ms}}^{-1}$
3. C.${\theta }_0={\sin }^{-1}\left(\frac{2}{\sqrt{5}}\right)$ and $v_0=\frac{3}{5}{\text{ ms}}^{-1}$
4. D.${\theta }_0={\sin }^{-1}\left(\frac{1}{\sqrt{5}}\right)$ and $v_0=\frac{5}{3}{\text{ ms}}^{-1}$

1. A.120 J
2. B.130 J
3. C.100 J
4. D.140 J

A particle is moving with speed $v=b\sqrt{x}$ along positive x-axis. Calculate the speed of the particle at time $t=\tau$ (assume that the particle is at origin $t=0$)

1. A.$\frac{b^2\tau }{\sqrt{2}}$
2. B.$b^2\tau$
3. C.$\frac{b^2\tau }{2}$
4. D.$\frac{b^2\tau }{4}$

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct ?

1. A.$R^2=h_1{h}_2$
2. B.$R^2=16h_1{h}_2$
3. C.$R^2=4h_1{h}_2$
4. D.$R^2=2h_1{h}_2$