Kinematics · JEE Main previous year questions

2020 12 questions

1. Q272020 · 6 Sept 2020 · Shift 2

   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.$60^{\circ }$
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   Answer: A

2. Q282020 · 6 Sept 2020 · Shift 2

   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.$0.41$
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   Answer: B

3. Q462020 · 6 Sept 2020 · Shift 2· Numerical answer

   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 ______ .

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   Answer: 9

4. Q392020 · 3 Sept 2020 · Shift 1

   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
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   Answer: A

5. Q472020 · 3 Sept 2020 · Shift 1· Numerical answer

   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 ($g=10\mathrm{m}{\mathrm{s}}^{-2}$) _______.

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   Answer: 150

6. Q312020 · 3 Sept 2020 · Shift 2
   
   1. A.
   2. B.
   3. C.
   4. D.
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   Answer: B

7. Q422020 · 3 Sept 2020 · Shift 2

   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.$\frac{2\pi }{\lambda }\left(\frac{L_2}{n_1}-\frac{L_1}{n_2}\right)$
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   Answer: A

8. Q372020 · 2 Sept 2020 · Shift 1

   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.$28.5{\text{ ms}}^{-1}$
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   Answer: B

9. Q322020 · 2 Sept 2020 · Shift 2
   
   1. A.(B), (C) and (D)
   2. B.(A), (B) and (C)
   3. C.(A) and (D)
   4. D.(A), (B) and (D)
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   Answer: B

10. Q382020 · 9 Jan 2020 · Shift 2

    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.$\frac{5}{8}\frac{u^2}{g}$
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    Answer: B

11. Q422020 · 8 Jan 2020 · Shift 2

    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
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    Answer: C

12. Q472020 · 7 Jan 2020 · Shift 1· Numerical answer
    
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    Answer: 10