Laws of Motion & Friction · JEE Main previous year questions

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2025 16 questions

Q372025 · 8 Apr 2025 · Shift 2
Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is $v_{1}$ , and that in the other string having radius of cross section R/2 is $v_{2}$ . Then $\frac{v _{2}}{v _{1}} =$
1. A. $8$
2. B. $4$
3. C. $2$
4. D. $2$
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Answer: C
Q442025 · 8 Apr 2025 · Shift 2
A block of mass $2 kg$ is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is $2 m$ and spring constant is $200 N/m$ . The block is pushed such that the length of the spring becomes $1 m$ and then released. At distance $x m$ ( $x < 2$ ) from the wall, the speed of the block will be
1. A. $10 [1 - (2 - x)^{2}]^{\frac{1}{2}} m / s$
2. B. $10 [1 - (2 - x)^{2}]^{\frac{3}{2}} m / s$
3. C. $10 [1 - (2 - x)^{2}] m / s$
4. D. $10 [1 - (2 - x)^{2}]^{2} m / s$
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Answer: A
Q382025 · 4 Apr 2025 · Shift 1
A body of mass $m$ is suspended by two strings making angles $θ_{1}$ and $θ_{2}$ with the horizontal ceiling with tensions $T_{1}$ and $T_{2}$ simultaneously. $T_{1}$ and $T_{2}$ are related by $T_{1} = 3 T_{2}$ , the angles $θ_{1}$ and $θ_{2}$ are
1. A. $θ_{1} = 3 0^{\circ} θ_{2} = 6 0^{\circ} with T_{2} = \frac{3 m g}{4}$
2. B. $θ_{1} = 4 5^{\circ} θ_{2} = 4 5^{\circ} with T_{2} = \frac{3 m g}{4}$
3. C. $θ_{1} = 3 0^{\circ} θ_{2} = 6 0^{\circ} with T_{2} = \frac{4 m g}{5}$
4. D. $θ_{1} = 6 0^{\circ} θ_{2} = 3 0^{\circ} with T_{2} = \frac{m g}{2}$
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Answer: D
Q462025 · 4 Apr 2025 · Shift 1· Numerical answer
A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $\frac{x}{5}$ where $x =$ ____.
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Answer: 4 or 3.5
Q382025 · 4 Apr 2025 · Shift 2
A block of mass $25 kg$ is pulled along a horizontal surface by a force at an angle $4 5^{\circ}$ with the horizontal. The friction coefficient between the block and the surface is 0.25 . The block travels at a uniform velocity. The work done by the applied force during a displacement of $5 m$ of the block is :
1. A. $490 J$
2. B. $970 J$
3. C. $735 J$
4. D. $245 J$
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Answer: D
Q362025 · 3 Apr 2025 · Shift 2
A block of mass $1 kg$ , moving along $x$ with speed $v_{i} = 10 m/s$ enters a rough region ranging from $x = 0.1 m$ to $x = 1.9 m$ . The retarding force acting on the block in this range is $F_{r} = - k x N$ , with $k = 10 N/m$ . Then the final speed of the block as it crosses rough region is.
1. A. $4 m/s$
2. B. $10 m/s$
3. C. $8 m/s$
4. D. $6 m/s$
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Answer: C
Q452025 · 2 Apr 2025 · Shift 1
1. A. $1.77 nC/m^{2}$
2. B. $0.885 nC/m^{2}$
3. C. $885 nC/m^{2}$
4. D. $17.7 nC/m^{2}$
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Answer: A
Q422025 · 2 Apr 2025 · Shift 2
1. A. $53, 5$
2. B. $53, 53$
3. C. $5, 5$
4. D. $5, 53$
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Answer: A
Q472025 · 2 Apr 2025 · Shift 2· Numerical answer
The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is__________m.
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Answer: 1
Q262025 · 28 Jan 2025 · Shift 1
1. A. $2 R g + \frac{k R ^{2}}{m}$
2. B. $3 R g + \frac{k R ^{2}}{m}$
3. C. $2 R g + \frac{4 k R ^{2}}{m}$
4. D. $2 g R + \frac{k R ^{2}}{m}$
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Answer: B
Q292025 · 24 Jan 2025 · Shift 1
A car of mass ' $m$ ' moves on a banked road having radius ' $r$ ' and banking angle $θ$ . To avoid slipping from banked road, the maximum permissible speed of the car is $v_{0}$ . The coefficient of friction $μ$ between the wheels of the car and the banked road is
1. A. $μ = \frac{v _{0}^{2} + r g t a n θ}{r g + v _{0}^{2} t a n θ}$
2. B. $μ = \frac{v _{0}^{2} - r g t a n θ}{r g - v _{0}^{2} t a n θ}$
3. C. $μ = \frac{v _{0}^{2} - r g t a n θ}{r g + v _{0}^{2} t a n θ}$
4. D. $μ = \frac{v _{0}^{2} + r g t a n θ}{r g - v _{0}^{2} t a n θ}$
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Answer: C
Q352025 · 24 Jan 2025 · Shift 2
The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation
1. A. $E^{2} = pc^{2} + m^{2} c^{4}$
2. B. $E^{2} = pc^{2} + m^{2} c^{2}$
3. C. $E^{2} = p^{2} c^{2} + m^{2} c^{4}$
4. D. $E^{2} = p^{2} c^{2} + m^{2} c^{2}$
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Answer: C
Q372025 · 24 Jan 2025 · Shift 2
A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_{1}$ and $t_{2}$ , respectively, then
1. A. $t_{1} < t_{2}$
2. B. $t_{1} = 2 t_{2}$
3. C. $t_{1} > t_{2}$
4. D. $t_{1} = t_{2}$
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Answer: A
Q482025 · 24 Jan 2025 · Shift 2· Numerical answer
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Answer: 36
Q262025 · 23 Jan 2025 · Shift 2
The equation of a transverse wave travelling along a string is $y (x, t) = 4.0 sin [20 \times 1 0^{- 3} x + 600 t] mm$ , where $x$ is in $mm$ and $t$ is in second. The velocity of the wave is :
1. A. $- 60 m/s$
2. B. $+ 60 m/s$
3. C. $+ 30 m/s$
4. D. $- 30 m/s$
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Answer: D
Q322025 · 22 Jan 2025 · Shift 1
1. A.4
2. B.1
3. C.2
4. D.3
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Answer: C