JEE Mains · Physics · STD 12 - Ray optics and optical instruments
- JEE Mains 2018
- Hard
- MCQ
A particle is oscillating on the \(X-\) axis with an amplitude \(2\, cm\) about the point \(x_0 = 10\, cm\) with a frequency \(\omega \). A concave mirror of focal length \(5\,
cm\) is placed at the origin ( see figure) Identify the correct statements \((A)\) The image executes periodic motion \((B)\) The image executes non-periodic motion \((C)\) The turning points of the image are asymmetric w.r.t the image of the point at \(x =10\,cm\) \((D)\) The distance between the turning points of the oscillation of the image is \(\frac{{100}}{{21}}\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \((A), (C), (D)\)
Step-by-step Solution
Detailed explanation
When object is at \(8\,\mathrm{cm}\)
Image \(V_{1}=\frac{f \times u}{u-f}=\frac{5 \times 8}{8-5}=-\frac{40}{3}\, \mathrm{cm}\)
When object is at \(12\,\mathrm{cm}\)
Image \(V_{2}=\frac{f \times u}{u-f}=\frac{5 \times 12}{12-5}=-\frac{60}{7}\, \mathrm{cm}\)
Separation \(=\left|\mathrm{V}_{1}-\mathrm{V}_{2}\right|=\frac{40}{3}-\frac{60}{7}=\frac{100}{21} \mathrm{cm}\)
So \(A,\,C\) and \(D\) are correct statements.
More questions from Physics
- A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to \(4\) times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particleJEE Mains 2022 Medium
- If \(\vec{E}\) and \(\vec{K}\) represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by : \((\omega-\) angular frequency) :JEE Mains 2023 Medium
- The distance of centre of mass from end \(A\) of a one dimensional rod \(( AB )\) having mass density \(\rho=\rho_{0}\left(1-\frac{ x ^{2}}{ L ^{2}}\right)\,kg / m\) and length \(L\) (in meter) is \(\frac{3 L }{\alpha} m\). The value of \(\alpha\) is \(\ldots \ldots \ldots . .\) (where \(x\) is the distance form end \(A\) )JEE Mains 2022 Hard
- Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius \(5^{\text {th}}\) orbit of the electron in \(\mathrm{Li}^{2+}\) and \(\mathrm{He}^{+}\) is _______.JEE Mains 2025 Easy
- Moment of inertia of a rod of mass ' M ' and length 'L' about an axis passing through its center and normal to its length is ' \(\alpha\) '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :JEE Mains 2025 Medium
- A cubic block of mass \(m\) is sliding down on an inclined plane at \(60^{\circ}\) with an acceleration of \(\frac{\mathrm{g}}{2}\), the value of coefficient of kinetic friction isJEE Mains 2025 Easy
More PYQs from JEE Mains
- Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across \(\mathrm{A}\) and \(B\), their readings are \(V_1, V_2\) and \(V_3\). Choose the correct option.
JEE Mains 2024 Hard - A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now ..... \(f\)JEE Mains 2016 Medium
- Given below are two statements: Statement \(I:\) For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases. Statement \(II:\) Escape velocity is independent of the radius of the planet. In the light of above statements, choose the most appropriate answer from the options given below on :JEE Mains 2023 Medium
- A solid sphere with uniform density and radius R is rotating initially with constant angular velocity \(\left(\omega_1\right)\) about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become \(R / 2\) is \(x \omega_1\). The value of \(x\) is ________JEE Mains 2025 Medium