Laws of Motion & Friction · JEE Main previous year questions

2026 23 questions

1. Q302026 · 6 Apr 2026 · Shift 1

   A lift of mass $1600\mathrm{kg}$ is supported by thick iron wire. If the maximum stress which the wire can withstand is $4\times 10^{8}N/{\mathrm{m}}^2$ and its radius is $4\mathrm{mm}$, then maximum acceleration the lift can take is ____ $m/{\mathrm{s}}^2$. (take $g=10m/{\mathrm{s}}^2$ and $\pi =3.14$)

   1. A.2.56
   2. B.3.89
   3. C.4.32
   4. D.5.16
   Show answer

   Answer: A

2. Q322026 · 6 Apr 2026 · Shift 1

   A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height $h$ as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height $h=\alpha R$. The value of $\alpha$ is ____.

   
   1. A.2
   2. B.4
   3. C.3
   4. D.6
   Show answer

   Answer: B

3. Q442026 · 6 Apr 2026 · Shift 2
   
   1. A.$7.74$
   2. B.$7.20$
   3. C.$6.55$
   4. D.$4.50$
   Show answer

   Answer: A

4. Q462026 · 6 Apr 2026 · Shift 2· Numerical answer

   A block takes $t$ time to slide down a plane inclined at $45^{\circ }$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $\frac{t}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\frac{\alpha }{100}\right)$. The value of $\alpha$ is ________.

   Show answer

   Answer: 75

5. Q292026 · 5 Apr 2026 · Shift 1
   
   1. A.5/3
   2. B.2/3
   3. C.3/5
   4. D.2/5
   Show answer

   Answer: A

6. Q302026 · 5 Apr 2026 · Shift 1
   
   1. A.2
   2. B.4
   3. C.$\sqrt{2}$
   4. D.$2\sqrt{2}$
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   Answer: A

7. Q282026 · 5 Apr 2026 · Shift 2

   A mass of $1\mathrm{kg}$ is kept on a inclined plane with $30^{\circ }$ inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of $4m/s$. The work done by the frictional force in time $2\mathrm{s}$ is ____ $\mathrm{J}$. (Take $g=10m/{\mathrm{s}}^2$)

   1. A.20
   2. B.25
   3. C.30
   4. D.10
   Show answer

   Answer: A

8. Q282026 · 4 Apr 2026 · Shift 1

   The time taken by a block of mass $m$ to slide down from the highest point to the lowest point on a rough inclined plane is $50\%$ more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at $45^{\circ }$ with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is _________.

   1. A.$3/4$
   2. B.$2/3$
   3. C.$5/9$
   4. D.$4/9$
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   Answer: C

9. Q342026 · 4 Apr 2026 · Shift 1

   A string $A$ of length $0.314\text{ m}$ and Young's modulus $2\times 10^{10}{\text{ N/m}}^2$ is connected to another string $B$ of length and Young's modulus both twice of those of $A$. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass $0.8\text{ kg}$. The net change in length of the combination is ________ $\text{mm}$. (radius of both the strings is $0.2\text{ mm}$ and acceleration due to gravity $=10{\text{ m/s}}^2$) (Mass of both strings is to be neglected as compared to the mass of load)

   1. A.3
   2. B.2
   3. C.1.9
   4. D.1
   Show answer

   Answer: B

10. Q312026 · 4 Apr 2026 · Shift 2

    A metal string $A$ is suspended from a rigid support and its free end is attached to a block of mass $M$. Second block having mass $2\mathrm{M}$ is suspended at the bottom of the first block using a string $B$. The area of cross sections of strings $A$ and $B$ are same. The ratio of lengths of strings of $A$ to $B$ is 2 and the ratio of their Young's moduli $(Y_A/Y_B)$ is 0.5. The ratio of elongations in $A$ to $B$ is ____.

    1. A.1
    2. B.4
    3. C.8
    4. D.6
    Show answer

    Answer: D

11. Q282026 · 2 Apr 2026 · Shift 2
    
    1. A.3.33
    2. B.3.12
    3. C.2.22
    4. D.1.42
    Show answer

    Answer: C

12. Q302026 · 28 Jan 2026 · Shift 1

    A block of mass $5\mathrm{kg}$ is moving on an inclined plane which makes an angle of $30^{\circ }$ with the horizontal. Friction coefficient between the block and inclined plane surface is $\frac{\sqrt{3}}{2}$. The force to be applied on the block so that the block will move down without acceleration is ____ $\mathrm{N}$. ($g=10m/{\mathrm{s}}^2$).

    1. A.25
    2. B.12.5
    3. C.15
    4. D.7.5
    Show answer

    Answer: B

13. Q322026 · 28 Jan 2026 · Shift 2
    
    1. A.$\sqrt{\frac{2L}{g\sin \theta -a_0\cos \theta }}$
    2. B.$\sqrt{\frac{4L}{g\sin 2\theta -a_0(1+\cos 2\theta )}}$
    3. C.$\sqrt{\frac{2L}{g\sin 2\theta -a_0(1+\cos 2\theta )}}$
    4. D.$\sqrt{\frac{4L}{g{\cos }^2\theta -a_0\sin \theta \cos \theta }}$
    Show answer

    Answer: B

14. Q422026 · 28 Jan 2026 · Shift 2
    
    1. A.20
    2. B.5
    3. C.30
    4. D.27
    Show answer

    Answer: C

15. Q262026 · 24 Jan 2026 · Shift 1

    A cylindrical block of mass $M$ and area of cross section $A$ is floating in a liquid of density $\rho$ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is ____

    1. A.$2\pi \sqrt{\frac{\rho A}{Mg}}$
    2. B.$\pi \sqrt{\frac{2M}{\rho Ag}}$
    3. C.$2\pi \sqrt{\frac{M}{\rho Ag}}$
    4. D.$\pi \sqrt{\frac{\rho A}{Mg}}$
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    Answer: C

16. Q382026 · 24 Jan 2026 · Shift 1

    Two masses $400\mathrm{g}$ and $350\mathrm{g}$ are suspended from the ends of a light string passing over a heavy pulley of radius $2\mathrm{cm}$ . When released from rest the heavier mass is observed to fall $81\mathrm{cm}$ in $9\mathrm{s}$ . The rotational inertia of the pulley is ____ $\mathrm{kg}\cdot {\mathrm{m}}^2$. $\left(g=9.8m/{\mathrm{s}}^2\right)$

    1. A.$8.3\times 10^{-3}$
    2. B.$4.75\times 10^{-3}$
    3. C.$1.86\times 10^{-2}$
    4. D.$9.5\times 10^{-3}$
    Show answer

    Answer: D

17. Q462026 · 24 Jan 2026 · Shift 1· Numerical answer
    
    Show answer

    Answer: 190 or 210

18. Q332026 · 23 Jan 2026 · Shift 1
    
    1. A.$3:4$
    2. B.$1:4$
    3. C.$2:3$
    4. D.$1:2$
    Show answer

    Answer: A

19. Q282026 · 23 Jan 2026 · Shift 2

    The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross section area of $17{\text{ cm}}^2$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by $4^{\circ }\text{C}$, then the piston will move _____ cm. (atmospheric pressure $=10^5\text{ Pa}$)

    1. A.1.55
    2. B.14.5
    3. C.15.5
    4. D.1.45
    Show answer

    Answer: C

20. Q312026 · 23 Jan 2026 · Shift 2
    
    1. A.$t_P<t_Q$
    2. B.$t_P=t_Q$
    3. C.$t_P>1.25t_Q$
    4. D.$t_P>t_Q$
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    Answer: A

21. Q312026 · 21 Jan 2026 · Shift 1

    Two strings $(A,B)$ having linear densities ${\mu }_A=2\times 10^{-4}kg/m$ and, ${\mu }_B=4\times 10^{-4}kg/m$ and lengths $L_A=2.5\mathrm{m}$ and $L_B=1.5\mathrm{m}$ respectively are joined. Free ends of $A$ and $B$ are tied to two rigid supports $C$ and $D$, respectively creating a tension of $500\mathrm{N}$ in the wire. Two identical pulses, sent from $C$ and $D$ ends, take time $t_1$ and $t_2$, respectively, to reach the joint. The ratio $t_1/t_2$ is:

    1. A.1.90
    2. B.1.18
    3. C.1.08
    4. D.1.67
    Show answer

    Answer: B

22. Q442026 · 21 Jan 2026 · Shift 1
    
    1. A.$mg/s$
    2. B.$mg/4$
    3. C.$mg$
    4. D.$mg/2$
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    Answer: B

23. Q442026 · 21 Jan 2026 · Shift 2
    
    1. A.$\frac{(M-m)g}{\left[\left(\frac{8}{3}\right)M+m\right]}$
    2. B.$\frac{(M-m)g}{2M+m}$
    3. C.$\frac{(M-m)g}{M+m}$
    4. D.$\frac{(M-m)g}{\left[\left(\frac{13}{6}\right)M+m\right]}$
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    Answer: A