JEE Mains · Physics · STD 11 - Work,energy,power and collision
- JEE Mains 2019
- Hard
- MCQ
A block of mass \(m\), lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant \(k\). The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a constant force \(F\), the maximum speed of the block is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(\frac{F}{{\sqrt {mk} }}\)
Step-by-step Solution
Detailed explanation
When \(\,{v_{\max }}\) \(\Rightarrow \) acceleration \(= 0\)
\( \Rightarrow \,x = \frac{F}{K}\)
Apply work energy theorem
\(\,{W_{sp}}\) + \(w_f\) = \(\Delta K.E\)
\(\begin{array}{l}
- \frac{1}{2}K{x^2} + F.x = \Delta K.E\,\,\,;\,\, - \frac{1}{2}K\frac{{{F^2}}}{{{K^2}}} + \frac{{{F^2}}}{K}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{2}mu_{\max }^2\\
\frac{{{F^2}}}{{2K}} = \frac{1}{2}mu_{\max }^{2\,}\,\,\,;\,\,\,\frac{F}{{\sqrt {mK} }} = {V_{\max }}
\end{array}\)
More questions from Physics
- A soap bubble of radius \(3\, {cm}\) is formed inside the another soap bubble of radius \(6\, {cm}\). The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is .......... \({cm}\)
JEE Mains 2021 Hard - The time taken for the magnetic energy to reach \(25\, \%\) of its maximum value, when a solenoid of resistance \(R ,\) inductance \(L\) is connected to a battery, is :JEE Mains 2021 Hard
- 10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from \(P _1\) to \(P _2\) is \(\alpha\) Joule \(\left( P _1=21.7 Pa\right.\) and \(\left.P _2=30 Pa, C _{ v }=21 J / K . mol , R=8.3 J / mol . K \right)\). The value of \(\alpha\) is _________ .
JEE Mains 2026 Hard - If \(\varepsilon_0\) is the permittivity of free space and \(E\) is the electric field, then \(\varepsilon_0 E^2\) has the dimensions is _______.JEE Mains 2024 Medium
- 12 wires each having resistance \(2 \Omega\) are joined to form a cube. A battery of \(6 \mathrm{~V}\) emf is joined across point \(\mathrm{a}\) and \(\mathrm{c}\). The voltage difference between \(e\) and \(f\) is ______V.
JEE Mains 2024 Hard - Two charges \(7 \mu C\) and \(-2 \mu C\) are placed at \((-9,0,0) cm\) and \((9,0,0) cm\) respectively in an external field \(E=\frac{ A }{ r ^2} \hat{ r }\), where \(A=9 \times 10^5 N / C . m ^2\).
Considering the potential at infinity is 0 , the electrostatic energy of the configuration is ___________ J .JEE Mains 2026 Medium
More PYQs from JEE Mains
- A small square loop of wire of side \(l\) is placed inside a large square loop of wire \(L(L \gg l)\). Both loops are coplanar and their centres coincide at point \(O\) as shown in figure. The mutual inductance of the system is.
JEE Mains 2022 Hard - Consider a long thin conducting wire carrying a uniform current I. A particle having mass " M " and charge " \(q\) " is released at a distance " \(a\) " from the wire with a speed \(v_0\) along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance \(x\) from the wire. The value of \(x\) is [ \(\mu_0\) is vacuum permeability]JEE Mains 2025 Hard
- An oscillating \(LC\) circuit consists of a \(75\,mH\) inductor and a \(1.2\,\mu F\) capacitor. If the maximum charge to the capacitor is \(2.7\,\mu C\). The maximum current in the circuit will be \(...........\,mA\).JEE Mains 2023 Medium
- Consider the following radioactive decay process \({ }_{84}^{218} A \stackrel{\alpha}{\longrightarrow} A_1 \stackrel{\beta^{-}}{\longrightarrow} A_2 \stackrel{\gamma}{\longrightarrow} A_3 \stackrel{\alpha}{\longrightarrow} A_4 \stackrel{B^{+}}{\longrightarrow} A_5 \stackrel{\gamma}{\longrightarrow} A_6\) The mass number and the atomic number \(A _6\) are given byJEE Mains 2023 Medium