JEE Mains · Physics · STD 12 -Electromagnetic induction
- JEE Mains 2019
- Hard
- Numerical
A thin strip \(10\, cm\) long is on a \(U\) shaped wire of negligible resistance and it is connected to a spring of spring constant \(0.5\,Nm^{-1}\) (see figure). The assembly is kept in a uniform magnetic field of \(0.1\, T\). If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of \(e\) is \(N\). If the mass of the strip is \(50\, grams\), its resistance \(10\,\Omega \) and air drag negligible, \(N\) will be close to
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(5000\)
Step-by-step Solution
Detailed explanation
\(\mathrm{T}_{0}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}=\frac{2 \pi}{\sqrt{10}}\)
\(\mathrm{A}=\mathrm{A}_{0} \mathrm{e}^{-1 / \gamma}\)
\(\therefore\) for \(\mathrm{A}=\frac{\mathrm{A}_{0}}{\mathrm{e}}, \mathrm{t}=\gamma\)
\(\mathrm{t}=\gamma=\frac{2 \mathrm{m}}{\mathrm{b}}=\frac{\frac{2 \mathrm{m}}{\mathrm{B}^{2} \ell^{2}}}{\frac{\mathrm{B}^{2} \ell^{2}}{\mathrm{R}}}=10^{4} \,\mathrm{s}\)
\(\therefore \) No of oscillation \(\frac{\mathrm{t}}{\mathrm{T}_{0}}=\frac{10^{4}}{2 \pi / \sqrt{10}} \approx 5000\)
More questions from Physics
- in circular plate of mass \(M\) and radius \(R\) has its density varying as \(p\left( r \right) = {p_0}\,r\) with \(P_0\) as constant and \(r\) is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is \(I = aMR^2\) . The value of the coefficient \(a\) isJEE Mains 2019 Hard
- Which of the following statement is not correct in the case of light emitting diodes? \(A.\) It is a heavily doped p-n junction. \(B.\) It emits light only when it is forward biased. \(C.\) It emits light only when it is reverse biased. \(D.\) The energy of the light emitted is equal to or slightly less than the energy gap of the semiconductor used. Choose the correct answer from the options given below :JEE Mains 2023 Medium
- Match List\(-I\) with List\(-II.\)
Choose the most appropriate answer from the option given below :List\(-I\) List\(-II\) \((a)\) Torque \((i)\) \({MLT}^{-1}\) \((b)\) Impulse \((ii)\) \({MT}^{-2}\) \((c)\) Tension \((iii)\) \({ML}^{2} {T}^{-2}\) \((d)\) Surface Tension \((iv)\) \({MI} {T}^{-2}\) JEE Mains 2021 Medium - A metallic surface is illuminated with radiation of wavelength \(\lambda\), the stopping potential is \(V_0\). If the same surface is illuminated with radiation of wavelength \(2 \lambda\), the stopping potential becomes \(\frac{V_0}{4}\). The threshold wavelength for this metallic surface will be -JEE Mains 2023 Medium
- An object is dropped from a height \(h\) from the ground. Every time it hits the ground it looses \(50\%\) of its kinetic energy. The total distance covered as \(t \to \infty \) isJEE Mains 2017 Hard
- The position of a particle as a function of time \(t\), is given by \(x\left( t \right) = at+ b{t^2} - c{t^3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will beJEE Mains 2019 Hard
More PYQs from JEE Mains
- An ice cube of dimensions \(60\,cm \times 50\,cm \times 20\,cm\) is placed in an insulation box of wall thickness \(1\,cm\). The box keeping the ice cube at \(0^{\circ}\,C\) of temperature is brought to a room of temperature \(40^{\circ}\,C\). The rate of melting of ice is approximately. (Latent heat of fusion of ice is \(3.4 \times 10^{5}\,J\,kg ^{-1}\) and thermal conducting of insulation wall is \(0.05\,Wm ^{-10} C ^{-1}\) )JEE Mains 2022 Hard
- A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance \(2.5 \mu \mathrm{~F}\). The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _____ \(\mathrm{Vs}^{-1}\).JEE Mains 2025 Hard
- The space between the plates of a parallel-plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants \(K _1=2, K_2=3\), and \(K _3=5\) (as shown in the figure). If new capacitance is \(\frac{ n }{3} C\) then the value of \(n\) is ___________.
JEE Mains 2026 Medium - Space between two concentric conducting spheres of radii \(a\) and \(b (b > a)\) is filled with \(a\) medium of resistivity \(\rho \). The resistance between the two spheres will beJEE Mains 2019 Hard
- If an air bubble of diameter \(2\) mm rises steadily through a liquid of density \(2000\) kg/m\(^3\) at a rate of \(0.5\) cm/s, then the coefficient of viscosity of liquid is _______ Poise. (Take \(g = 10\) m/s\(^2\))JEE Mains 2026 Hard