201860 marks18 questions
7 of its 18 questions are here. The rest have a figure or are still being checked, so for now they're only in the official PDF.
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Source: JEE (Advanced) 2018, Paper 1, Physics, published by JEE (Advanced). The official PDF
The potential energy of a particle of mass m at a distance r from a fixed point O is given by V(r) = kr²/2, where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point O. If v is the speed of the particle and L is the magnitude of its angular momentum about O, which of the following statements is (are) true?
Consider a body of mass 1.0 kg at rest at the origin at time t = 0. A force F⃗ = (αt î + β ĵ) is applied on the body, where α = 1.0 N s⁻¹ and β = 1.0 N. The torque acting on the body about the origin at time t = 1.0 s is τ⃗. Which of the following statements is (are) true?
A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height h in the capillary tube above the water surface in the beaker. The surface tension of water is σ. The angle of contact between water and the wall of the capillary tube is θ. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?
Two vectors A⃗ and B⃗ are defined as A⃗ = a î and B⃗ = a (cos ωt î + sin ωt ĵ), where a is a constant and ω = π/6 rad s⁻¹. If |A⃗ + B⃗| = √3|A⃗ − B⃗| at time t = τ for the first time, the value of τ, in seconds, is __________.
Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0 m s⁻¹ and the man behind walks at a speed 2.0 m s⁻¹. A third man is standing at a height 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz. The speed of sound in air is 330 m s⁻¹. At the instant, when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is __________.
A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle 60° with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is (2 − √3)/√10 s, then the height of the top of the inclined plane, in metres, is __________. Take g = 10 m s⁻².
Sunlight of intensity 1.3 kW m⁻² is incident normally on a thin convex lens of focal length 20 cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in kW m⁻², at a distance 22 cm from the lens on the other side is __________.