Practice Questions

Q21.A particle is moving along the x -axis with its coordinate with time t given by x(t) = 10 + 8t −3t2. Another particle is moving along the y -axis with its coordinate as a function of time given by y(t) = 5 −8t3. At t = 1 s, the speed of the second particle as measured in the frame of the first particle is given as √v. Then v(in m s−1) is ___________.

Q21.A body of mass 2 kg is driven by an engine delivering a constant power of 1 J s−1. the body starts from rest and moves in a straight line. After 9 s, the body has moved a distance (in m)….

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 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.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:

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.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.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.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. 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.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.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.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 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.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 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.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 ____________

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.A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to ______

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.Four resistance 40 Ω, 60 Ω, 90 Ω 110 Ω and make the arms of a quadrilateral ABCD. Across AC is a battery of emf 40 V and internal resistance negligible. The potential difference across BD in V is __________

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.Initially a gas of diatomic molecules is contained in a cylinder of volume V1 at a pressure P1 and temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature 2000 K, when contained in a volume 2V1 is given by P2 . The ratio P2/P1 is -

Q23.Three containers C1, C2 and C3 have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during the process) JEE Main 2020 (08 Jan Shift 2) JEE Main Previous Year Paper C1 C2 C3 T 1l 2l −− 60oC −− 1l 2l 30oC 2l −− 1l 60oC 1l 1l 1l θ The value of θ (in oC to the nearest integer) is___________