Oscillations (SHM) · JEE Main previous year questions

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2021 24 questions

Q452021 · 1 Sept 2021 · Shift 2
1. A. $10 m/ s^{2}$
2. B. $5 m/ s^{2}$
3. C. $4 m/ s^{2}$
4. D. $9.8 m/ s^{2}$
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Answer: C
Q462021 · 26 Aug 2021 · Shift 2
If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is :
1. A.86.4 s
2. B.4.32 s
3. C.43.2 s
4. D.8.64 s
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Answer: C
Q532021 · 26 Aug 2021 · Shift 2· Numerical answer
If the maximum value of accelerating potential provided by a radio frequency oscillator is 12 kV. The number of revolutions made by a proton in a cyclotron to achieve one sixth of the speed of light is ............... [ $m_{p} = 1.67 \times 1 0^{- 27} kg$ , $e = 1.6 \times 1 0^{- 19} C$ , Speed of light $= 3 \times 1 0^{8} m/s$ ]
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Answer: 543
Q542021 · 26 Aug 2021 · Shift 2· Numerical answer
The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum of known mass 'm' to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3%, the accuracy to which E is known is ..............%
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Answer: 14
Q562021 · 26 Aug 2021 · Shift 2· Numerical answer
Two simple harmonic motions are represented by the equations $x_{1} = 5 sin (2 π t + \frac{π}{4})$ and $x_{2} = 52 (sin 2 π t + cos 2 π t)$ . The amplitude of second motion is ............... times the amplitude in first motion.
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Answer: 2
Q352021 · 27 Jul 2021 · Shift 2
An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant $t = \frac{T}{4} s$ starting from mean position. Assume that the initial phase of the oscillation is zero.
1. A.0.62 J
2. B. $6.2 \times 1 0^{- 3}$ J
3. C. $1.2 \times 1 0^{3}$ J
4. D. $6.2 \times 1 0^{3}$ J
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Answer: A
Q542021 · 27 Jul 2021 · Shift 2· Numerical answer
A particle executes simple harmonic motion represented by displacement function as $x (t) = A sin (ω t + ϕ)$ If the position and velocity of the particle at $t = 0 s$ are 2 cm and $2 ω cm s^{- 1}$ respectively, then its amplitude is $x 2 cm$ where the value of x is __________.
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Answer: 2
Q572021 · 25 Jul 2021 · Shift 1· Numerical answer
A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same charge 'q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x << 1 m), the particle executes SHM. Its angular frequency of oscillation will be ____ $\times 1 0^{5}$ rad/s if $q^{2} = 10 C^{2}$ .
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Answer: 6000
Q592021 · 25 Jul 2021 · Shift 1· Numerical answer
A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of $6 0^{\circ}$ to the vertical will be (g = $10 m/ s^{2}$ ) ____ m/s.
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Answer: 2
Q322021 · 25 Jul 2021 · Shift 2
In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.
1. A. $\frac{1}{2}$
2. B. $\frac{3}{4}$
3. C. $\frac{1}{3}$
4. D. $\frac{1}{4}$
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Answer: B
Q462021 · 22 Jul 2021 · Shift 2
$T_{0}$ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to $\frac{1}{16}$ times of its initial value, the modified time period is :
1. A. $4 T_{0}$
2. B. $\frac{1}{4} T_{0}$
3. C. $T_{0}$
4. D. $8 π T_{0}$
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Answer: B
Q522021 · 22 Jul 2021 · Shift 2· Numerical answer
Three students $S_{1}, S_{2}$ and $S_{3}$ perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table. | Student No. | Length of Pendulum (cm) | No. of oscillations (n) | Total time for n oscillations | Time period (s) | |---|---|---|---|---| | 1 | 64.0 | 8 | 128.0 | 16.0 | | 2 | 64.0 | 4 | 64.0 | 16.0 | | 3 | 20.0 | 4 | 36.0 | 9.0 | (Least count of length $= 0.1 cm$ and Least count for time $= 0.1 s$ ) If $E_{1}, E_{2}$ and $E_{3}$ are the percentage errors in 'g' for students 1, 2 and 3 respectively, then the minimum percentage error is obtained by student no. ________.
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Answer: 1
Q462021 · 18 Mar 2021 · Shift 1
The time period of a simple pendulum is given by $T = 2 π \frac{l}{g}$ . The measured value of the length of pendulum is 10 cm known to a 1mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to be nearest integer is :-
1. A. $2%$
2. B. $3%$
3. C. $5%$
4. D. $4%$
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Answer: B
Q512021 · 18 Mar 2021 · Shift 1· Numerical answer
A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $\frac{1}{a} s$ . The value of 'a' to the nearest integer is _______.
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Answer: 6
Q432021 · 18 Mar 2021 · Shift 2
The function of time representing a simple harmonic motion with a period of $\frac{π}{ω}$ is :
1. A. $cos (ω t) + cos (2 ω t) + cos (3 ω t)$
2. B. $sin^{2} (ω t)$
3. C. $sin (ω t) + cos (ω t)$
4. D. $3 cos (\frac{π}{4} - 2 ω t)$
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Answer: D
Q352021 · 16 Mar 2021 · Shift 1
Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g/2, the time period of pendulum will be :
1. A. $3 T$
2. B. $\frac{2}{3} T$
3. C. $\frac{T}{3}$
4. D. $\frac{3}{2} T$
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Answer: B
Q382021 · 26 Feb 2021 · Shift 1
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period :
1. A. $2 π \frac{R}{g}$
2. B. $\frac{g}{2 π R}$
3. C. $\frac{2 π R}{g}$
4. D. $\frac{1}{2 π} \frac{g}{R}$
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Answer: A
Q402021 · 26 Feb 2021 · Shift 1
If two similar springs each of spring constant $K_{1}$ are joined in series, the new spring constant and time period would be changed by a factor :
1. A. $\frac{1}{2}, 22$
2. B. $\frac{1}{4}, 22$
3. C. $\frac{1}{2}, 2$
4. D. $\frac{1}{4}, 2$
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Answer: C
Q412021 · 26 Feb 2021 · Shift 1
A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to $R^{3}$ . Its time period of revolution will be given by :
1. A. $T \propto R^{\frac{4}{3}}$
2. B. $T \propto R^{\frac{5}{2}}$
3. C. $T \propto R^{\frac{3}{2}}$
4. D. $T \propto R^{2}$
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Answer: D
Q452021 · 26 Feb 2021 · Shift 2
1. A. $\frac{M F}{F + M a}$
2. B. $\frac{F + M a}{M}$
3. C. $\frac{M a - F}{M}$
4. D. $\frac{F - M a}{M}$
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Answer: D
Q492021 · 26 Feb 2021 · Shift 2
Given below are two statements : Statement I : A second's pendulum has a time period of 1 second. Statement II : It takes precisely one second to move between the two extreme positions. In the light of the above statements, choose the correct answer from the options given below :
1. A.Both Statement I and Statement II are false
2. B.Statement I is false but Statement II is true
3. C.Both Statement I and Statement II are true
4. D.Statement I is true but Statement II is false
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Answer: B
Q532021 · 26 Feb 2021 · Shift 2· Numerical answer
Time period of a simple pendulum is T. The time taken to complete $\frac{5}{8}$ oscillations starting from mean position is $\frac{α}{β} T$ . The value of $α$ is _________.
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Answer: 7
Q432021 · 25 Feb 2021 · Shift 2
1. A. $2 π \frac{m}{k}$
2. B. $π \frac{m}{k}$
3. C. $2 π \frac{m}{2 k}$
4. D. $π \frac{m}{2 k}$
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Answer: B
Q442021 · 25 Feb 2021 · Shift 2
1. A.9.87 N
2. B.0.49 N
3. C.50 N
4. D.100 N
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Answer: A