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Assertion: In realistic situation, the `x-t, y-t and a-t` graphs will be smooth. Reason: Physically acceleration and velocity cannot change values abruptly at an

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Two projectiles A and B are projected with same speed at angles 30° and 60° to be horizontal then, which amongst the following relation between their range, maximum height and time of flight is

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A rigid body is rolling without slipping on the horizontal surface, then match the Column I with Column II and choose the correct option from the codes given below. Column I Column II A. Velocity at point `A, i.e. v_A` p.`vsqrt2` B. Velocity at point `B, i.e. v_B` q- zero C. Velocity at point `C, i.e. v_C` r. `v` D. Velocity at point `D, i.e. v_D` s. `2v`

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A particle executing S.H.N. along a straight line has a velocity of um/s when its displacement from mean position is 3 m and 3 m / s when displacement is 4m. Find the time taken to travel 2.5 m from the positive extremity of its

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A wine of density a g/`cm^3` is stretched between two clamps 1 m apart while subjected to an extension of 0.05 cm. What is the lowest frequency of transverse vibration in the wire? Let young’s Modulus = `y = 9 xx10^(10)N`/`m^2`

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A gas in equilibrium has uniform density and pressure throughout its volume. This is strictly true only if there are no external influences. A gas column under gravity, for example, does not have uniform density (and pressure). As you might expect, its density decreases with height. The precise dependence is given by the so-called law of atmospheres ` n^2` = `n^1` exp [ -mg (`h_2` – `h_1`)/ kB T] where` n-2`, `n-1` refer to number density at heights `h_2` and `h_1` respectively. Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column: `n_2`

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The figure given below depicts two circular motions. The radius of the circle, the period of revolution, the initial position and the sense of revolution are indicated in the figures. Obtain the simple harmonic motions of the x-projection of the radius vector of the rotating particle P in each case.

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Two stars each of one solar mass (= `2×10^(30)` kg) are approaching each other for a head on collision. When they are a distance 109 km, their speeds are negligible. What is the speed with which they collide ? The radius of each star is `10^4` km. Assume the stars to remain undistorted until they collide. (Use the known value of

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“Politics is the art of the possible”. Similarly, “Science is the art of the soluble”. Explain this beautiful aphorism on the nature and practice of

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A mass = m suspend separately from two springs of spring constant `k_1 and k_2` gives time period `t_1 and t_2` respectively. If the same mass is connected to both the springs as shown in figure. Calculate the time period ‘t’ of the combined

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A balloon is ascending at the rate of 4.9m/s. A pocket is dropped from the balloon when situated at a height of 245m. How long does it take the packet to reach the ground? What is its final

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What is meant by coefficient of friction and angel of friction? Establish the relation between the two? ORA block of mass 10kg is sliding on a surface inclined at a angle of `30^o` with the horizontal. Calculate the acceleration of the block. The coefficient of kinetic friction between the block and the surface is

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Show that `C_P - C_V = R` Where `[C_P =` specific heat at constant pressure ; `C_V =` specific heat at constant volume and R = Universal Gas constant] for an ideal

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A room has a 4m x 4m x10cm concrete roof `(K_1 = 1.26w|m|'^oC)`. At some instant, the temperature outside is `46^oc` and radius `32^oc`. 1) Calculate amount of heat flowing per second into the room through the roof. 2) If bricks `(K_2 – 0.56w |m|'^oc)` of thickness 7.5cm are laid down on roof, calculate the new rate of heat flow under the same temperature

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Two perfect gases at absolute temperature T1 and T2 are mixed. There is no loss of energy. Find the temperature of the mixture if the masses of molecules are `m_1 and m_2` and number of molecules is `n_1 and n_2`

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(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2M`R^2`/5, where M is the mass of the sphere and R is the radius of the sphere. (b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be M`R^2`/4, find its moment of inertia about an axis normal to the disc and passing through a point on its

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A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the metre

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Normally, the reported result of measurement is a number that includes all digits in the number that are known reliably plus first digit that is uncertain. The digits that are known reliably plus the first uncertain digit are known as significant digits or significant figures. e.g. When a measured distance is reported to be 374.5 m, it has four significant figures 3, 7, 4 and 5. The figures 3, 7, 4 are certain and reliable, while the digit 5 is uncertain. Clearly, the digits beyond the significant digits reported in any result are superfluous.`5.74 g` of a substance occupies `1.2

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Uniform Circular Motion When an object follows a circular path at a constant speed, the motion of the object is called uniform circular motion. The word uniform refers to the speed which is uniform (constant) throughout the motion. Although the speed does not vary, the particle is accelerating because the velocity changes its direction at every point on the circular track.The figure shows a particle P which moves along a circular track of radius `r` with a uniform speed `u`.Two cars `A and B` move along a concentric circular path of radius `r_A and r_B` with velocities `v_A and v_B`

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The force of gravitation

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