JEE Mains · Physics · STD 11 - Transmission of heat
- JEE Mains 2025
- Medium
- MCQ
The temperature of a body in air falls from \(40^{\circ} \mathrm{C}\) to \(24^{\circ} \mathrm{C}\) in 4 minutes. The temperature of the air is \(16^{\circ} \mathrm{C}\). The temperature of the body in the next 4 minutes will be:
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(\frac{56}{3}{ }^{\circ} \mathrm{C}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& \Delta T=T_2-T_1=16^{\circ} \mathrm{C} \\
& \text { And } T_0=16^{\circ} \mathrm{C} \\
& \frac{\Delta T}{t_1}=-k\left(32-16^{\circ}\right)...(i) \\
& \frac{\left(24-T_3\right)}{4}=-k\left(\frac{24+T_3}{2}-16\right) ....(ii) \\
& \frac{16}{4}=-k(16) \\
& \Rightarrow \frac{\left(24-T_3\right)}{4}=-k\left(12+\frac{T_3}{2}-16\right) \\
& \Rightarrow \frac{16}{24-T_3}=\frac{16}{T_3} T_2 \\
& \Rightarrow \frac{T_3}{2}-4=24-T_3 \\
& \Rightarrow \frac{3 T_3}{2}=28 \\
& \Rightarrow T_3=\frac{56}{3}{ }^{\circ} \mathrm{C}
\end{aligned}\)
& \Delta T=T_2-T_1=16^{\circ} \mathrm{C} \\
& \text { And } T_0=16^{\circ} \mathrm{C} \\
& \frac{\Delta T}{t_1}=-k\left(32-16^{\circ}\right)...(i) \\
& \frac{\left(24-T_3\right)}{4}=-k\left(\frac{24+T_3}{2}-16\right) ....(ii) \\
& \frac{16}{4}=-k(16) \\
& \Rightarrow \frac{\left(24-T_3\right)}{4}=-k\left(12+\frac{T_3}{2}-16\right) \\
& \Rightarrow \frac{16}{24-T_3}=\frac{16}{T_3} T_2 \\
& \Rightarrow \frac{T_3}{2}-4=24-T_3 \\
& \Rightarrow \frac{3 T_3}{2}=28 \\
& \Rightarrow T_3=\frac{56}{3}{ }^{\circ} \mathrm{C}
\end{aligned}\)
More questions from Physics
- Dimensions of universal gravitational constant \((G)\) in terms of Planck's constant \((h)\), distance \((L)\), mass \((M)\) and time \((T)\) are _______.JEE Mains 2026 Medium
- A conducting circular loop is placed in \(X - Y\) plane in presence of magnetic field \(\overrightarrow{ B }=\left(3 t ^{3} \hat{ j }+3 t ^{2} \hat{ k }\right)\) in SI unit. If the radius of the loop is \(1 m\), the induced emf in the loop, at time, \(t =2\,s\) is \(n \pi V\). The value of \(n\) is.JEE Mains 2022 Medium
- Charges \(-q\) and \(+ q\) located at \(A\) and \(B\), respectively, constitute an electric dipole. Distance \(AB = 2a\), \(O\) is the mid point of the dipole and \(OP\) is perpendicular to \(AB\). A charge \(Q\) is placed at \(P\) where \(OP = y\) and \(y >> 2a\). The charge \(Q\) experiences an electrostatic force \(F\). If \(Q\) is now moved along the equatorial line to \(P'\) such that \(OP' = \frac{y}{3}\), the force on \(Q\) will be close to: \(\left( {\frac{y}{3} > > 2a} \right)\)
JEE Mains 2019 Hard - When a gas filled in a closed vessel is heated by raising the temperature by \(1^{\circ} C\), its pressure increase by \(0.4 \%\). The initial temperature of the gas is ..........\(K\)JEE Mains 2022 Medium
- The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is \(n\) times higher than the moment of inertia of the given ring. Here, \(\mathrm{n}=\)_________
Consider all the bodies have equal masses.JEE Mains 2025 Hard - An electron gun is placed inside a long solenoid of radius \(\mathrm{R}\) on its axis. The solenoid has \(\mathrm{n}\) turns/length and carries a current \(I\). The electron gun shoots an electron along the radius of the solenoid with speed \(v\). If the electron does not hit the surface of the solenoid, maximum possible value of \({v}\) is (all symbols have their standard meaning)
JEE Mains 2020 Medium
More PYQs from JEE Mains
- Small water droplets of radius \(0.01 \mathrm{~mm}\) are formed in the upper atmosphere and falling with a terminal velocity of \(10 \mathrm{~cm} / \mathrm{s}\). Due to condensation, if \(8 \mathrm{such}\) droplets are coalesced and formed a larger drop, the new terminal velocity will be _______ \(\mathrm{cm} / \mathrm{s}\).JEE Mains 2024 Hard
- With rise in temperature, the Young's modulus of elasticity _______.JEE Mains 2024 Hard
- For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through \(O\) (the centre of mass) and \(O ^{\prime}(\) corner point \()\) is
JEE Mains 2020 Hard - A solid cylinder having radius \(R\) and length \(L\) is slipping on a rough horizontal plane. At time \(t=0\) the cylinder has a translational velocity \(v_0=49\) m/s, perpendicular to its axis and a rotational velocity \(v_0/4R\) about the centre. The time taken by the cylinder to start rolling is ________ seconds. (coefficient of kinetic friction \(\mu_K=0.25\) and \(g=9.8\) m/s\(^2\))JEE Mains 2026 Hard