Centre of Mass & Rotational Motion · JEE Main previous year questions

2026 33 questions

1. Q282026 · 22 Jan 2026 · Shift 1

   A cylindrical tube $AB$ of length $l$, closed at both ends contains an ideal gas of 1 mol having molecular weight $M$. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $AB$ and passing through the edge at end $A$, as shown in the figure. If $P_A$ and $P_B$ are the pressures at $A$ and $B$ respectively, then (Consider the temperature is same at all points in the tube)

   1. A.$P_B=P_A{e}^{\left(\frac{M{\omega }^2{l}^2}{3RT}\right)}$
   2. B.$P_B=P_A$
   3. C.$P_B=P_A{e}^{\left(\frac{M{\omega }^2{l}^2}{2RT}\right)}$
   4. D.$P_B=P_A{e}^{\left(\frac{M{\omega }^2{l}^2}{RT}\right)}$
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   Answer: C

2. Q342026 · 22 Jan 2026 · Shift 1

   A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm . The moment of inertia of this pair of spheres about the tangent passing through the point of contact is ____ $\mathrm{kg}\cdot {\mathrm{m}}^2$.

   1. A.0.18
   2. B.0.72
   3. C.0.36
   4. D.0.63
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   Answer: D

3. Q392026 · 22 Jan 2026 · Shift 1

   Three identical coils $C_1,C_2$ and $C_3$ are closely placed such that they share a common axis. $C_2$ is exactly midway. $C_1$ carries current $I$ in anti-clockwise direction while $C_3$ carries current $I$ in clockwise direction. An induced current flows through $C_2$ will be in clockwise direction when

   1. A.$C_1$ and $C_3$ move with equal speeds away from $C_2$
   2. B.$C_1$ moves towards $C_2$ and $C_3$ moves away from $C_2$
   3. C.$C_1$ and $C_3$ move with equal speeds towards $C_2$
   4. D.$C_1$ moves away from $C_2$ and $C_3$ moves towards $C_2$
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   Answer: B

4. Q502026 · 22 Jan 2026 · Shift 1· Numerical answer

   A circular disc has radius $R_1$ and thickness $T_1$. Another circular disc made of the same material has radius $R_2$ and thickness $T_2$. If the moment of inertia of both discs are same and $\frac{R_1}{R_2}=2$ then $\frac{T_1}{T_2}=\frac{1}{\alpha }$. The value of $\alpha$ is ____.

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   Answer: 16

5. Q302026 · 21 Jan 2026 · Shift 1

   An aluminium and steel rods having same lengths and cross-sections are joined to make total length of $120\mathrm{cm}$ at $30^{\circ }\mathrm{C}$. The coefficient of linear expansion of aluminium and steel are $24\times 10^{-6}{/}^{\circ }\mathrm{C}$ and $1.2\times 10^{-5}{/}^{\circ }\mathrm{C}$, respectively. The length of this composite rod when its temperature is raised to $100^{\circ }\mathrm{C}$, is ____ cm.

   1. A.120.20
   2. B.120.06
   3. C.120.15
   4. D.120.03
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   Answer: C

6. Q482026 · 21 Jan 2026 · Shift 1· Numerical answer
   
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   Answer: 17

7. Q282026 · 21 Jan 2026 · Shift 2

   A large drum having radius $R$ is spinning around its axis with angular velocity $\omega$, as shown in figure. The minimum value of $\omega$ so that a body of mass $M$ remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass $M$ as $\mu$, is :

   1. A.$\sqrt{\frac{2g}{\mu R}}$
   2. B.$\sqrt{\frac{g}{2\mu R}}$
   3. C.$\sqrt{\frac{\mu g}{R}}$
   4. D.$\sqrt{\frac{g}{\mu R}}$
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   Answer: D

8. Q352026 · 21 Jan 2026 · Shift 2

   Two cars A and B each of mass $10^3$ kg are moving on parallel tracks separated by a distance of 10 m, in same direction with speeds 72 km/h and 36 km/h. The magnitude of angular momentum of car A with respect to car B is ____ J·s.

   1. A.$3.6\times 10^5$
   2. B.$10^5$
   3. C.$3\times 10^5$
   4. D.$2\times 10^5$
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   Answer: B