JEE Mains · Physics · STD 11 - 5. work,energy,power and collision
An engine is attached to a wagon through a shock absorber of length \(1.5\, {m}\). The system with a total mass of \(40,000\, {kg}\) is moving with a speed of \(72\, {kmh}^{-1}\) when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by \(1.0\, {m}\). If \(90\, \%\) of energy of the wagon is lost due to friction, the spring constant is \(....\, \times 10^{5}\, {N} / {m}\)
- A \(16\)
- B \(400\)
- C \(1.6\)
- D \(160\)
Answer & Solution
Correct Answer
(A) \(16\)
Step-by-step Solution
Detailed explanation
\(\text { Work }=\Delta K . E\) \(W_{\text {friction }}+W_{\text {spring }}=0-\frac{1}{2} m v^{2}\) \(-\frac{90}{100}\left(\frac{1}{2} m v^{2}\right)+W_{\text {Spring }}=-\frac{1}{2} m v^{2}\) \({W}_{\text {spring }}=-\frac{10}{100} \times \frac{1}{2} {mv}^{2}\)…
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 \(600\,pF\) capacitor is charged by \(200\,V\) supply. It is then disconnected from the supply and is connected to another uncharged \(600\,pF\) capacitor. Electrostatic energy lost in the process is \(.........\,\mu J\).JEE Mains 2023 Hard
- In a spring gun having spring constant \(100\, {N} / {m}\) a small ball \('B'\) of mass \(100\, {g}\) is put in its barrel (as shown in figure) by compressing the spring through \(0.05\, {m}\). There should be a box placed at a distance \('d'\) on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of \(2\, {m}\) above the ground. The value of \(d\) is \(....{m} .\) \(\left(g=10\, {m} / {s}^{2}\right)\)
JEE Mains 2021 Hard - If \(\in\), \( E \) and \( t \) represent the free space permittivity, electric field and time respectively, then the unit of \( \frac{eE}{t} \) will be :JEE Mains 2026 Medium
- A train moves towards a stationary observer with speed \(34\, m/s\). The train sounds a whistle and its frequency registered by the observer is \(f_1\). If the speed of the train is reduced to \(17\, m/s\), the frequency registered is \(f_2\). If speed of sound is \(340\, m/s\), then the ratio \(f_1/f_2\) isJEE Mains 2019 Hard
- Monochromatic light of wavelength \(500 \mathrm{~nm}\) is used in Young's double slit experiment. An interference pattern is obtained on a screen When one of the slits is covered with a very thin glass plate (refractive index \(=1.5\) ), the central maximum is shifted to a position previously occupied by the \(4^{\text {th }}\) bright fringe. The thickness of the glass-plate is _______\(\mu \mathrm{m}\).JEE Mains 2024 Hard
- An insulated copper wire of \(100\) turns is wrapped around a wooden cylindrical core of the crosssectional area \(24\,cm ^2\). The two ends of the wire are connected to a resistor. The total resistance in the circuit is \(12\,\Omega\). If an externally applied uniform magnetic field in the core along its axis changes from \(1.5 T\) in one direction to \(1.5\,T\) in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be \(.........\,mC\).JEE Mains 2023 Medium
More PYQs from JEE Mains
- The distance of the point \((-1,9,-16)\) from the plane \(2 x+3 y-z=5\) measured parallel to the line \(\frac{x+4}{3}=\frac{2-y}{4}=\frac{z-3}{12}\) is \(......\)JEE Mains 2023 Hard
- Light ray incident along a vector \(\vec{AO}\) \((\vec{AO} = 2\hat{i}-3\hat{j})\) emerges out along vector \(\vec{OB}\) \((\vec{OB} = C\hat{i}-4\hat{j})\) as shown in the figure below. The value of \(C\) is ________.
JEE Mains 2026 Hard - If \( x^{2}+x+1=0 \) then the value of \( (x+\frac{1}{x})^{4}+(x^{2}+\frac{1}{x^{2}})^{4}+(x^{3}+\frac{1}{x^{3}})^{4}+...+(x^{25}+\frac{1}{x^{25}})^{4} \) is:JEE Mains 2026 Medium
- A parallel plate capacitor of capacitance \(12.5 \mathrm{pF}\) is charged by a battery connected between its plates to potential difference of \(12.0 \mathrm{~V}\). The battery is now disconnected and a dielectric slab \(\left(\epsilon_{\mathrm{r}}=6\right)\) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _______.\(\times 10^{-12} \mathrm{~J}\).JEE Mains 2024 Hard
- Let \(S=\left\{(x, y) \in N \times N : 9(x-3)^{2}+16(y-4)^{2} \leq 144\right\}\) and \( T=\left\{(x, y) \in R \times R :(x-7)^{2}+(y-4)^{2} \leq 36\right\}\) Then \(n ( S \cap T )\) is equal to \(......\)JEE Mains 2022 Hard
- When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, \(4^{\text {th}}\) mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and \(5^{\text {th}}\) division of vernier scale coincides with a main scale division. Measured length of cylinder is ___________ mm. (Least count of Vernier calliper \(= 0.1\ mm\))JEE Mains 2026 Easy