Inequalities L-3 | Operations on Intervals (Part A) | By Naman Agarwal | JEE Mains and Advanced | CBSE

A uniform thin rod AB of length L and mass m is undergoing rotation about a fixed axis passing through end A and perpendicular to the rod, such that end A remains stationary as shown. The kinetic energy of section AP of the rod is equal to the kinetic energy of section BP of the rod at an instant. Then what is the value of ((AB)/(Ap))^(3)? (AB and AP are lengths of respectively parts of the rod)

Imagine a system, that can keep the room temperature within a narrow range between 20^@C to 25^@C . The system includes a heat engine operating with variable power P = 3KT, where K is a constant coefficient, depending upon the thermal insulation of the room, the area of the walls and the thickness of the walls. T is temperature of the room in temperature drops lower than 20^@C , the engine turns on, when the temperature increase over 25^@ C, the engine turns off, room looses energy at a rate of K(T - T_0), T_0 is the outdoor temperature. The heat capacity of the room is C. Given (T_0=10^@C, ln(3/2) =0.4 , ln(6/5)=0.18 , C/K =750 SI-unit) Suppose at t = 0, the engine turns off, after how much time interval, again, the engine will turn on

Imagine a system, that can keep the room temperature within a narrow range between 20^@C to 25^@C . The system includes a heat engine operating with variable power P = 3KT, where K is a constant coefficient, depending upon the thermal insulation of the room, the area of the walls and the thickness of the walls. T is temperature of the room in temperature drops lower than 20^@C , the engine turns on, when the temperature increase over 25^@ C, the engine turns off, room looses energy at a rate of K(T - T_0), T_0 is the outdoor temperature. The heat capacity of the room is C. Given (T_0=10^@C, ln(3/2) =0.4 , ln(6/5)=0.18 , C/K =750 SI-unit) Suppose at t = 0, the engine turns on, after how much time interval again, the engine will turn off