A projectile is launched at an angle 'α' with the horizontal with a velocity 20 ms-1. After 10 s, its inclination with horizontal is 'β'. The value of tan β will be: (g = 10 ms-2)
Two masses m and m/2 are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system (see figure). Because of torsional constant k, the restoring torque is τ = kθ for angular displacement θ. If the rod is rotated by θ0 and released, the tension in it when it passes through its mean position will be:
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An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to [Use g = 10 ms-2]
A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is:
A particle is projected upward from the surface of earth (radius = R) with a speed equal to the orbital speed of a satellite near the earth’s surface. The height to which it would rise is
A block of mass m is placed on a surface with a vertical cross-section given by y = x3/6. If the coefficient of friction is 0.5, then the maximum height above the ground at which the block can be placed without slipping is
One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, 27°C. The work done on the gas will be:
A solid sphere of mass M and radius R is lying on a rough horizontal plane. A constant force F = 4Mg acts vertically at point P such that OP makes an angle of 60° with horizontal. Find the minimum value of coefficient of friction μμ so that sphere starts pure rolling.
What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10-3 Pa s, respectively.
(Density of water: 103 kg/m3)
An electric bulb is rated as 200 W. What will be the peak magnetic field at 4 m distance produced by the radiation coming from this bulb? Consider this bulb as a point source with 3.5% efficiency.
A spring of spring constant 5 × 103 is stretched initially by 5 cm from the unstretched position. The work required to stretch it further by another 5 cm is
When ethylbromide and n-propyl bromide is allowed to react with sodium, in ether, they form
Which of the following favours the backward reaction in a chemical equilibrium?
What is the main reason for the fact that carboxylic acids can undergo ionization?
A heat engine absorbs heat Q1 at temperature T1 and heat Q2 at temperature T2. Work done by the engine is (Q1 + Q2). This data
In the presence of acid, the hydrolysis of methyl cyanide gives
The hormone which controls the process like burning of fats, proteins and carbohydrates to liberate energy in the body is
The chemical equilibrium of a reversible reaction is not influenced by
Which of the following is produced by reaction of RCN in sodium and alcohol ?
The range of the function f(x) = [x] − x, where [x] denotes the greatest integer ≤ x, is
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