JEE Mains · Physics · STD 11 - 5. work,energy,power and collision
In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg , moving in opposite directions with speeds of \(10 m / s\) and \(30 m / s\), respectively, strike each other and stick together. The rise in temperature (in \({ }^{\circ} C\) ), if all the heat produced during the collision is retained by these spheres, is :
(specific heat of sphere material \(31 cal / kg .{ }^{\circ} C\) and \(1 cal =4.2 J)\)
- A 1.75
- B 1.44
- C 1.15
- D 1.95
Answer & Solution
Correct Answer
(B) 1.44
Step-by-step Solution
Detailed explanation
\(( K . E )_{\text {lost }}=\frac{1}{2} \mu V_{ rel }^2\left(1- e ^2\right)\) \(=\frac{1}{2}\left(\frac{m_1 m_2}{m_1+ m _2}\right)(10+30)^2(1-0)\) \(=\frac{1}{2}\left[\frac{(15)(25)}{40}\right][40]^2\) \(=7500 J\) \(( K . E )_{ loss }=\left( m _1+ m _2\right)( S )(\Delta T )\)…
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
- Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool.
\(\left(\right.\)Take \(g=10 \mathrm{~m} / \mathrm{s}^2\), specific heat of water \(\left.=4200 \mathrm{~J} /(\mathrm{kg} \mathrm{K})\right)\)JEE Mains 2025 Medium - A bead \(P\) sliding on a frictionless semi-circular string \((A C B)\) and it is at point \(S\) at \(t =0\) and at this instant the horizontal component of its velocity is \(v\). Another bead \(Q\) of the same mass as \(P\) is ejected from point \(A\) at \(t =0\) along the horizontal string \(A B\), with the speed \(v\), friction between the beads and the respective strings may be neglected in both cases. Let \(t_p\) and \(t_Q\) be the respective times taken by beads \(P\) and \(Q\) to reach the point \(B\), then the relation between \(t_p\) and \(t_Q\) is
JEE Mains 2026 Hard - A body of mass \(m\) is moving in a circular orbit of radius \(R\) about a planet of mass \(M\). At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius \(\frac{R}{2}\) , and the other mass, in a circular orbit of radius \(\frac{3R}{2}\). The difference between the final and initial total energies isJEE Mains 2018 Hard
- A light wave described by \(E =60 \sin \left(3 \times 10^{15}\right) t + \sin \left(12 \times 10^{15}\right)\) t] (in SI units) falls on a metal surface of work function 2.8 eV . The maximum kinetic energy of ejected photoelectron is (approximately) _________ eV .JEE Mains 2026 Medium
- A projectile is launched at an angle ' \(\alpha\) ' with the horizontal with a velocity \(20 \; ms ^{-1}\). After \(10 s\), its inclination with horizontal is ' \(\beta\) '. The value of \(\tan \beta\) will be : \(\left( g =10 \; ms ^{-2}\right)\)JEE Mains 2022 Hard
- A galvanometer having a coil resistance of \(100\ \Omega\). gives a full scale deflection, when a currect of \(I\ mA\) is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of \(10\ A\), is :......\(Ω\)JEE Mains 2016 Medium
More PYQs from JEE Mains
- If the lines \(\frac{{x - 2}}{1} = \frac{{y - 3}}{1} = \frac{{z - 4}}{{ - k}}\) and \(\frac{{x - 1}}{k} = \frac{{y - 4}}{2} = \frac{{z - 5}}{1}\) are coplanar then \(k \) can haveJEE Mains 2013 Easy
- If the equation of the parabola, whose vertex is at \((5,4)\) and the directrix is \(3 x+y-29=0\), is \(x^{2}+a y^{2}+b x y+c x+d y+k=0\) then \(a + b + c + d + k\) is equal toJEE Mains 2022 Hard
- Let \( S=\{z\in\mathbb{C}:4z^{2}+\overline{z}=0\} \) Then \( \sum_{z\in S}|z|^{2} \) is equal to:JEE Mains 2026 Medium
- Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is __________.JEE Mains 2026 Medium
- Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as \(4.62 \mathrm{~s}, 4.632 \mathrm{~s}, 4.6 \mathrm{~s}\) and \(4.64 \mathrm{~s}\). The arithmetic mean of these reading in correct significant figure is _______.JEE Mains 2024 Hard
- The distance of the point \((2,3)\) from the line \(2 \mathrm{x}-\) \(3 \mathrm{y}+28=0\), measured parallel to the line \(\sqrt{3} \mathrm{x}-\mathrm{y}+1=0\), is equal toJEE Mains 2024 Medium