Practice Questions

Q21.A ball is dropped from the top of a 100 m high tower on a planet. In the last 21 s before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in m s−2 ) near the surface on that planet is______

Q21.The centre of mass of a solid hemisphere of radius 8 cm is x cm from the centre of the flat surface. Then value of x is

Q21.A particle (m = 1kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2m ). After reaching C, the particle continues to move freely in air as a projectile. When it reaching its highest point P (height 1m ), the kinetic energy of the particle (in J ) is: (Figure drawn is schematic and not to scale; take g = 10ms−2 ) ______________.

Q21.A particle of mass 200 MeV c−2 collides with a hydrogen atom at rest. Soon after the collision, the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV ) is N4 . The value of N is: (Given the mass of the hydrogen atom to be 1 GeV c−2 )......... → + 2ˆj + m . Then the magnitude of torque about the point N acts at a point (4ˆi + 3ˆj −ˆk)

Q22.A non-isotropic solid metal cube has coefficients of linear expansion as: 5 × 10−5/oC along the x-axis and 5 × 10−6/oC along the y and the z-axis. If the coefficient of volume expansion of the solid is C × 10−6/oC then the value of C is _____________

Q22.A force F = (ˆi 3ˆk) m will be √x N −m. The value of x is.......... (ˆi + 2ˆj + ˆk)

Q22.A thin rod of mass 0. 9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0. 1 kg moving in a straight line with velocity 80 m s−1 hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad s−1) of the rod immediately after the collision will be …………

Q22.An massless equilateral triangle EFG of side 'a' (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is N ma2 where N is an integer. The value of N is ___________ . 20

Q22.A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm ) of the platform when the person reaches its centre....

Q22.A circular disc of mass M and radius R is rotating about its axis with angular speed ω1 . If another stationary disc having radius R and same mass M is dropped co-axially on to the rotating disc. Gradually both discs 2 attain constant angular speed ω2 . The energy lost in the process is p% of the initial energy. Value of p is ______

Q22. Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is μ = 0.4 , the maximum possible value of 100 × ba for a box not to topple before moving is ________

Q22.One end of a straight uniform 1m long bar is pivoted on horizontal table. It is released from rest when it makes an angle 30o from the horizontal (see figure). Its angular speed when it hits the table is given as √n rad s−1 , where n is an integer. The value of n is ____________

Q22.An electric field E = 4xˆi −(y2 + 1)ˆjN/C passes through the box shown in figure. The flux of the electric field through surfaces ABCD and BCGF are marked as ϕI and ϕII respectively. The difference between (ϕI −ϕII) is (in Nm2/C ) ____________.

Q22.A body A of mass m = 0.1 kg has an initial velocity of 3ˆi m s−1 . It collides elastically with another body B of the same mass which has an initial velocity of 5ˆj m s−1 . After the collision, A moves with a velocity m s−1 . The energy of B after the collision is written as 10x J. The value of x is →v= 4(ˆi +ˆj)

Q22.Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial velocities of the two bodies (in degree) is -

Q22.The change in the magnitude of the volume of an ideal gas when a small additional pressure ΔP is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity ΔT at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm respectively. If |ΔT| = C|ΔP| then value of C in (K/ atm) is __________

Q22.A particle of mass m is moving along the x-axis with initial velocity uˆi. It collides elastically with a particle of mass 10m at rest and then moves with half its initial kinetic energy (see figure). If sin θ1 = √n sin θ2 then value of n is ________. JEE Main 2020 (02 Sep Shift 2) JEE Main Previous Year Paper

Q22.An asteroid is moving directly towards the centre of the earth. When at a distance of 10R ( R is the radius of the earth) from the centre of the earth, it has a speed of 12 km s−1. Neglecting the effect of earth's atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km s−1) ? Give your answer to the nearest integer in km s−1 __________.

Q22.An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to

Q22.An engine takes in 5 moles of air at 20 °C and 1 atm, and compresses it adiabatically to 1/10th of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be XkJ. The value of X to the nearest integer is:

Q23.A Carnot engine operates between two reservoirs of temperatures 900K and 300K . The engine performs 1200J of work per cycle. The heat energy (in J ) delivered by the engine to the low temperature reservoir, in a cycle, is _____________ JEE Main 2020 (07 Jan Shift 1) JEE Main Previous Year Paper

Q23.Two concentric circular coils, C1 and C2 , are placed in the XY plane. C1 has 500turns, and a radius of 1 cm . C2 has 200 turns and radius of 20 cm . C2 carries a time dependent current I(t) = (5t2 −2t + 3)A where t is in s. The emf induced in C1(in mV) at the instant t = 1 s is x4 . The value of x is ..........

Q23.Nitrogen gas is at 300 °C temperature. The temperature (in K ) at which the rms speed of a H2 molecule would be equal to the rms speed of a nitrogen molecule, is … … … . (Molar mass of N2 gas 28 g ).

Q23.If minimum possible work is done by a refrigerator in converting 100 grams of water at 0 °C to ice, how much heat (in calories) is released to the surroundings at temperature 27 °C (Latent heat of ice = 80 Cal / gram) to the nearest integer?

Q23.A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. What is the maximum angular speed (in rad s−1 ) with which it can be rotated about its other end in a space station without breaking the wire? [Breaking stress of wire (σ)= 4.8 × 107 N m−2 and area of cross-section of the wire = 10−2 cm2 ]