JEE Mains · Physics · STD 11 - 5. work,energy,power and collision
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 \(200 \mathrm{~N} / \mathrm{m}\). The block is pushed such that the length of the spring becomes 1 m and then released. At distance \(\mathrm{x} \mathrm{m}(\mathrm{x} \lt 2)\) from the wall. the speed of the block will be :
- A \(10[1-(2-x)]^{3 / 2} \mathrm{~m} / \mathrm{s}\)
- B \(10\left[1-(2-x)^2\right]^{1 / 2} \mathrm{~m} / \mathrm{s}\)
- C \(10\left[1-(2-\mathrm{x})^2\right] \mathrm{m} / \mathrm{s}\)
- D \(10\left[1-(2-\mathrm{x})^2\right]^2 \mathrm{~m} / \mathrm{s}\)
Answer & Solution
Correct Answer
(B) \(10\left[1-(2-x)^2\right]^{1 / 2} \mathrm{~m} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
Given, Natural length of spring \(=2 \mathrm{~m}\) Initial compression in spring \(\left(\mathrm{x}_{\mathrm{i}}\right)=1 \mathrm{~m}\) Final compression in spring \(\left(\mathrm{x}_{\mathrm{f}}\right)=(2-\mathrm{x}) \mathrm{m}\) Using energy conservation…
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 light ray enters a solid glass sphere of refractive index \(\mu=\sqrt{3}\) at an angle of incidence \(60^{\circ}\). The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is......JEE Mains 2020 Hard
- A potentiometer wire \(AB\) having length \(L\) and resistance \(12\, r\) is joined to a cell \(D\) of \(emf\) \(\varepsilon \) and internal resistance \(r\). A cell \(C\) having \(emf\) \(\varepsilon /2\) and internal resistance \(3r\) is connected. The length \(AJ\) at which the galvanometer as shown in figure shows no deflection is
JEE Mains 2019 Medium - The displacement equations of two interfering waves are given by \(y_1 =10 \sin \left(\omega t+\frac{\pi}{3}\right) cm\) \(y_2 =5[\sin (\omega t)+\sqrt{3} \cos \omega t] \;cm\) respectively. The amplitude of the resultant wave is \(.............cm\).JEE Mains 2023 Hard
- For plan electromagnetic waves propagating in the \(z-\) direction, which one of the following combination gives the correct possible direction for \(\vec E\) and \(\vec B\) field respectively?JEE Mains 2015 Medium
- In a nuclear fission reaction of an isotope of mass \(M\), three similar daughter nucler of same mass are formed. The speed of a daughter nuclei in terms of mass defect \(\Delta \mathrm{M}\) will be _______.JEE Mains 2024 Hard
- Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as \(V ^q\), where \(V\) is the volume of the gas. The value of \(q\) is \(\left( {\gamma = \frac{{{C_P}}}{{{C_V}}}} \right)\)JEE Mains 2015 Hard
More PYQs from JEE Mains
- If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at \(440^{\text {th }}\) position in this arrangement, is :JEE Mains 2025 Easy
- Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{d y}{d x}=\frac{y}{x}\left(1+x y^2\left(1+\log _e x\right)\right)\) \(x > 0, y(1)=3\). Then \(\frac{y^2(x)}{9}\) is equal to :JEE Mains 2023 Hard
- Consider two sets \(A\) and \(B\), each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of B be 36 and q respectively. Let d and D be the common differences of AP's in A and B respectively such that \(D=d+3, d \gt 0\). If \(\frac{p+q}{p-q}=\frac{19}{5}\), then \(p-q\) is equal toJEE Mains 2025 Medium
- Let \(\alpha, \beta, \gamma\) and \(\delta\) be the coefficients of \(x^7, x^5, x^3\) and \(x\) respectively in the expansion of \(\left(x+\sqrt{x^3-1}\right)^5+\left(x-\sqrt{x^3-1}\right)^5, x\gt1\). If u and v satisfy the equations
\(\begin{aligned}
& \alpha u+\beta v=18 \\
& \gamma u+\delta v=20
\end{aligned}\)
then \(u+v\) equals :JEE Mains 2025 Hard - The sum of all values of \(\theta \, \in \,\left( {0,\frac{\pi }{2}} \right)\) satisfying \({\sin ^2}\,2\theta + {\cos ^4}\,2\theta = \frac{3}{4}\) isJEE Mains 2019 Hard
- If the number of seven-digit numbers, such that the sum of their digits is even, is \(m \cdot n \cdot 10^{\mathrm{n}}\); \(m, n \in\{1,2,3, \ldots, 9\}\), then \(m+n\) is equal to _______JEE Mains 2025 Easy