JEE Mains · Physics · STD 11 - 13. oscillations
The velocity of a particle executing simple harmonic motion along \(x\)-axis is described as \(v^2 = 50 - x^2\), where \(x\) represents displacement. If the time period of motion is \(\dfrac{x}{7}\) s, the value of \(x\) is _____.
- A 40
- B 44
- C 48
- D 52
Answer & Solution
Correct Answer
(B) 44
Step-by-step Solution
Detailed explanation
The given equation is \(v^2 = 50 - x^2\) Differentiating with respect to \(x\): \(2v \dfrac{dv}{dx} = -2x\) \(v \dfrac{dv}{dx} = -x\) Since acceleration \(a = v \dfrac{dv}{dx}\), we get: \(a = -x\) Comparing this with the standard equation of SHM \(a = -\omega^2 x\), we get:…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A thin prism with angle \( 5^{\circ} \) of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is ___________.JEE Mains 2026 Medium
- If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be _______ hours \(30\) minutes.JEE Mains 2024 Hard
- A man in a car at location \(Q\) on a straight highway is moving with speed \(v\). He decides to reach a point \(P\) in a field at a distance \(d\) from highway (point \(M\) ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance \(RM\), so that the time taken to reach \(P\) is minimum?
JEE Mains 2018 Hard - In Young's double slit arrangement, slits are separated by a gap of \(0.5\, mm ,\) and the screen is placed at a distance of \(0.5\, m\) from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of \(5890\, A^o\) isJEE Mains 2021 Hard
- Steel ruptures when a shear of \(3 .5 \times 10^8\,\,N\,m^{-2}\) is applied. The force needed to punch a \(1\,cm\) diameter hole in a steel sheet \(0.3\,cm\) thick is nearlyJEE Mains 2014 Medium
- Three harmonic waves having equal frequency \(\mathrm{v}\) and same intensity \(\mathrm{I}_{0}\), have phase angles \(0 , \frac{\pi}{4}\) and \(-\frac{\pi}{4}\) respectively. When they are superimposed the intensity of the resultant wave is close toJEE Mains 2020 Medium
More PYQs from JEE Mains
- If the line \(\frac{2-x}{3}=\frac{3 y-2}{4 \lambda+1}=4-z\) makes a right angle with the line \(\frac{x+3}{3 \mu}=\frac{1-2 y}{6}=\frac{5-z}{7}\), then \(4 \lambda+9 \mu\) is equal to :JEE Mains 2024 Medium
- As per the given figure, two blocks each of mass \(250\,g\) are connected to a spring of spring constant \(2\,Nm ^{-1}\). If both are given velocity \(V\) in opposite directions, then maximum elongation of the spring is:
JEE Mains 2022 Hard - A cube is placed inside an electric field, \(\overrightarrow{{E}}=150\, {y}^{2}\, \hat{{j}}\). The side of the cube is \(0.5 \,{m}\) and is placed in the field as shown in the given figure. The charge inside the cube is \(.....\times 10^{-11} {C}\)
JEE Mains 2021 Hard - Let \(a_1 , a_2, a_3, .... , a_n\), be in \(A.P\). If \(a_3 + a_7 + a_{11} + a_{15} = 72\) , then the sum of its first \(17\) terms is equal toJEE Mains 2016 Hard
- If the least and the largest real values of \(\alpha,\) for which the equation \(z+\alpha|z-1|+2 i=0\) \(( z \in C\) and \(i=\sqrt{-1}\) ) has a solution, are \(p\) and \(q\) respectively; then \(4\left( p ^{2}+ q ^{2}\right)\) is equal to ..........JEE Mains 2021 Hard
- An electric dipole of moment \(\overrightarrow{\mathrm{p}}=(-\hat{\mathrm{i}}-3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}) \times 10^{-29}\; \mathrm{C} \cdot \mathrm{m}\) is at the origin \((0,0,0) .\) The electric field due to this dipole at \(\overrightarrow{\mathrm{r}}=+\hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}\) (note that \(\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{p}}=0)\) is parallel toJEE Mains 2020 Medium