JEE Mains JEE Advance BITSAT
JEE Mains | PYQ

Year

All years 2025 2024 2023 2022 2021

An automobile of mass '\( m \)' accelerates starting from origin and initially at rest, while the engine supplies constant power \( P \). The position is given as a function of time by:

Given below is the plot of a potential energy function \( U(x) \) for a system, in which a particle is in one dimensional motion, while a conservative force \( F(x) \) acts on it. Suppose that \( E_{\text{mech}} = 8 \, \text{J} \), the incorrect statement for this system is:

[where K.E. = kinetic energy]

A small block slides down from the top of hemisphere of radius \( R = 3 \, \text{m} \) shown in the figure. The height ‘\( h \)’ at which the block will lose contact with the surface of the sphere is ________ \( \text{m} \).
(Assume there is no friction between the block and the hemisphere)

An engine is attached to a wagon through a shock absorbed of length \( 1.5\,\text{m} \). The system with a total mass of \( 40{,}000\,\text{kg} \) is moving with a speed of \( 72\,\text{km}\,\text{h}^{-1} \) when the brakes are applied to bring it to rest. In the process of the system being through to rest, the spring of the shock absorber gets compressed by \( 1.0\,\text{m} \). If \( 90\% \) of energy of the wagon is lost due to friction, the spring constant is ______ \( \times 10^5\,\text{N/m} \).

A pendulum bob has a speed of \( 3 \, \text{m/s} \) at its lowest position. The pendulum is \( 50 \, \text{cm} \) long. The speed of bob, when the length makes an angle of \( 60^\circ \) to the vertical will be \( (g = 10 \, \text{m/s}^2) \), ____________ \( \text{m/s} \).

A body of mass \( m \) dropped from a height \( h \) reaches the ground with a speed of \( 0.8\sqrt{g h} \). The value of work done by the air-friction is:

Statement I: A cyclist is moving on an unbanked road with a speed of \( 7 \, \text{km h}^{-1} \) and takes a sharp circular turn along a path of radius of \( 2 \, \text{m} \) without reducing the speed. The static friction coefficient is \( 0.2 \). The cyclist will not slip and pass the curve. \( (g = 9.8 \, \text{m s}^{-2}) \)
Statement II: If the road is banked at angle of \( 45^\circ \), cyclist can cross the curve of \( 2 \, \text{m} \) radius with the speed of \( 18.5 \, \text{km h}^{-1} \) without slipping.
In the light of the above statements, choose the correct answer from the options given below.

← PreviousQuestion 6 of 7Next →

JEE Main 2021 1st September Evening Shift

A body of mass \( m \) dropped from a height \( h \) reaches the ground with a speed of \( 0.8\sqrt{g h} \). The value of work done by the air-friction is: