JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius r = 0.1 m. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended through a height of 3.6 m is __________ m/s. (Assume string does not slip and \( g=10 m/s^{2} \))
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Using energy conservation \( \frac{1}{2}mv^{2}+\frac{1}{2}2mv^{2}+\frac{1}{2}\frac{30mR^{2}}{2}\times\frac{v^{2}}{R^{2}}=mgh \) \( 9\,mv^{2}=mgh \) \( v=\sqrt{\frac{gh}{9}}=\sqrt{\frac{10\times3.6}{9}} \) \( v=\sqrt{4}=2\,m/s \)
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
- The angle of deviation through a prism is minimum when \((A)\) Incident ray and emergent ray are symmetric to the prism \((B)\) The refracted ray inside the prism becomes parallel to its base \((C)\) Angle of incidence is equal to that of the angle of emergence \((D)\) When angle of emergence is double the angle of incidence Choose the correct answer from the options given below
JEE Mains 2021 Medium - A radar sends an electromagnetic signal of electric field \(\left( E _{0}\right)=2.25\,V / m\) and magnetic field \(\left( B _{0}\right)=1.5 \times 10^{-8}\,T\) which strikes a target on line of sight at a distance of \(3\,km\) in a medium After that, a pail of signal \((echo)\) reflects back towards the radar vitli same velocity and by same path. If the signal was transmitted at time \(t_{0}\) from radar. then after how much time (in \(\times 10^{-5}\,s\)) echo will reach to the radar?JEE Mains 2022 Medium
- An object is placed at a distance of \(12 \,{cm}\) from a convex lens. A convex mirror of focal length \(15 \,{cm}\) is placed on other side of lens at \(8 \,{cm}\) as shown in the figure. Image of object coincides with the object.When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be ..... \((cm)\)
JEE Mains 2021 Hard - \(\frac{x}{x+4}\) is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its \((i)\) third permitted energy level to the second level and \((ii)\) the highest permitted energy level to the second permitted level. The value of \(x\) will be.JEE Mains 2022 Medium
- The nuclear activity of a radioactive element becomes \(\left(\frac{1}{8}\right)^{\text {th }}\) of its initial value in \(30\, years.\) The half-life of radioactive element is \(....\,years.\)JEE Mains 2021 Medium
- The equivalent resistance between \(A\) and \(B\) is \(......\)
JEE Mains 2023 Medium
More PYQs from JEE Mains
- If \(P\) is a \(3 \times 3\) real matrix such that \(P ^{ T }=a P +( a -1) I\), where \(a > 1\), then \(..........\)JEE Mains 2023 Hard
- A particle of charge \(16\times10^{-16}\, C\) moving with velocity \(10\, ms^{-1}\) along \(x-\) axis enters a region where magnetic field of induction \(\vec B\) is along the \(y-\) axis and an electric field of magnitude \(10^4\, Vm^{-1}\) is along the negative \(z-\) axis. If the charged particle continues moving along \(x-\) axis, the magnitude of \(\vec B\) isJEE Mains 2013 Medium
- Let \(y=y(x)\) be the solution curve of the differential equation \(\sin \left(2 x^{2}\right) \log _{c}\left(\tan x^{2}\right) d y+\left(4 x y-4 \sqrt{2} x \sin \left(x^{2}-\frac{\pi}{4}\right)\right) d x=0\) \(0 < x < \sqrt{\frac{\pi}{2}}\), which passes through the point \(\left(\sqrt{\frac{\pi}{6}}, 1\right)\). Then \(\left|y\left(\sqrt{\frac{\pi}{3}}\right)\right|\) is equal to \(.....\)JEE Mains 2022 Hard
- A bakelite beaker has volume capacity of \(500\, cc\) at \(30^{\circ} C\). When it is partially filled with \(V _{ m }\) volume (at \(30^{\circ}\) ) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If \(\gamma_{\text {(beaker) }}=6 \times 10^{-6}{ }^{\circ} C ^{-1}\) and \(\gamma_{(\text {mercury })}=1.5 \times 10^{-4}{ }^{\circ} C ^{-1},\) where \(\gamma\) is the coefficient of volume expansion, then \(V _{ m }(\)in \(cc )\) is close toJEE Mains 2020 Hard
- A block of mass 5 kg is moving on an inclined plane which makes an angle of \(30^{\circ}\) with the horizontal. Friction coefficient between the block and inclined plane surface is \(\frac{\sqrt{3}}{2}\). The force to be applied on the block so that the block will move down without acceleration is ___________ N.JEE Mains 2026 Medium
- A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is:JEE Mains 2026 Medium