JEE Main entrance exam Question Bank Solutions for Physics (JEE Main)

An object is projected in the air with initial velocity u at an angle θ. The projectile motion is such that the horizontal range R, is maximum.

Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be ______ degree.

A ball is projected from the ground with a speed 15 ms^-1 at an angle θ with horizontal so that its range and maximum height are equal, then tan θ will be equal to ______.

The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target the rifle must be aimed in order to hit the target?

A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms^-1. The coefficient of friction between the surface and bock is 0.5. The distance covered by the block before coming to rest is ______.

[use g = 9.8 ms^-2]

A body starts from rest on a long inclined plane of slope 45°. The coefficient of friction between the body and the plane varies as µ = 0.3 x, where x is distance travelled down the plane. The body will have maximum speed (for g = 10 m/s²) when x = ______.

The entropy of any system is given by `S = alpha^2betaIn[(mukR)/(Jbeta^2) + 3]` Where α and β are the constants µ J, k, and R are no. of moles, the mechanical equivalent of heat, Boltzmann constant, and gas constant respectively. `["take S" = (dQ)/T]`

Choose the incorrect option from the following.

The workdone by a gas molecule in an x' isolated system is given by, W = αβ² `e^(-x^2/(alpha"KT"))`, where x is the displacement, k is the Boltzmann constant and T is the temperature. α and β are constants. Then the dimensions of β will be ______.

The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30° banked road at maximum possible speed without skidding is ______ × 10³ kg m/s².

[Given cos30° = 0.87, µ_s = 0.2]

A wave is represented by y = a sin(At - Bx + C) where A, B, C are constants and t is in seconds and x is in metre. The Dimensions of A, B, and C are ______.

A certain element decays in two different ways - it shows alpha decay with a half life of (ln 2) years and with beta decay, it has a half life of (ln 4) years. After how many years will a pure sample of 100 mg of the element would have 50 mg of that element?

An air bubble in glass slab (µ = 1.5) when viewed from one side, appears to be at 6 cm and from opposite side 4 cm. The thickness of glass slab is ______.

All the surfaces are frictionless. Strings are light and frictionless. The tension in string 1 is ______ N. (Take g = 10 m/s²)

A particle is given an initial speed u inside a smooth spherical shell of radius R = 1 m that it is just able to complete the circle. Acceleration of the particle when its velocity is vertical is ______.

The mirror of length 2l makes 10 revolutions per minute about the axis crossing its mid-point O and perpendicular to the plane of the figure There is a light source in point A and an observer at point B of the circle of radius R drawn around centre O (∠AOB = 90°) What is the proportion `"R"/ℓ` if the observer B first sees the light source when the angle of mirror ψ = 15°?

If the critical angle for total internal reflection from a medium to vacuum is 30°, the velocity of light in the medium is ______.

P = `alpha/beta` exp `(-"az"/"K"_"B"theta)`

θ `→` Temperature

P `→` Pressure

K_B `→` Boltzmann constant

z `→` Distance

Dimension of β is ______.

A small bead of mass m can move on a smooth circular wire (radius R) under the action of a force F = `"Km"/"r"^2` directed (r = position of bead r from P and K = constant) towards a point P within the circle at a distance R/2 from the centre. The minimum velocity should be ______ m/s of bead at the point of the wire nearest the centre of force (P) so that bead will complete the circle. (Take `"k"/(3"R")` = 8 unit) 

A disc of radius 5 cm rolls on a horizontal surface with linear velocity v = 1`hat"i"` m/s and angular velocity 50 rad/s. Height of particle from ground on rim of disc which has velocity in vertical direction is ______ cm.

A wet open umbrella is held upright and is rotated about the handle at a uniform rate of 21 revolutions in 44 s. If the rim of the umbrella is a circle of 1 metre in diameter and the height of the rim above the floor is 1.5 m, the drops of water spun off the rim and hit the floor at a horizontal ______ m from the umbrella.

Two spherical mirrors, one convex and the other concave, each of same radius of curvature R are arranged coaxially at a distance of 2R from each other. A small circle of radius a is drawn on the convex mirror as shown in figure. What is the radii of first two images of the circle?