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Two forces `F_1= 3 hati - 4 hatj and F_2 = 2 hati - 3 hatj` are acting upon a body of mass `2 kg`. Find the force `F_3`, which when acts on the body will make it
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A system consists of three masses `m_1, m_2 and m_3` connected by a string passing over a pulley `P`. The mass `m_1` hangs freely and `m_2 and m_3` are on a rough horizontal table (the coefficient of friction = `mu`.The pulley is frictionless and of negligible mass. The downward acceleration of mass `m_1` is (Assume, `m_1 = m_2 = m_3 =
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Assertion: A spring of force constant `k` is cut into two pieces having lengths in the ratio 1 : 2. The force constant of series combination of the two parts is `2k'/'3`. Reason: The spring connected in series are represented by `k= k_1+
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Work A farmer ploughing the field, a construction worker carrying bricks, a student studying for a competitive examination, an artist painting a beautiful landscape, all are said to be working. In physics, however, the word ‘Work’ covers a definite and precise meaning. Work refers to the force and the displacement over which it acts. Consider a constant force `F` acting on an object of mass `m`. The object undergoes a displacement `d` in the positive `x`-direction as shown in figure.The work done by the force is defined to be the product of component of the force in the direction of
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Kinetic Energy The energy possessed by a body by virtue of its motion is called kinetic energy. In other words, the amount of work done, a moving object can do before coming to rest is equal to its kinetic energy.`.^..' '` Kinetic energy, `KE =1/2mv^2` where, `m` is a mass and `v` is the velocity of a body.The units and dimensions of KE are Joule (in SI) and `[ML^2T^(-2)]`, respectively. Kinetic energy of a body is always positive. It can never be negative.The kinetic energy of an air molecule `(10^(-21) J)` in `eV`
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There are many types of spring. Important among these are helical and spiral springs as shown in figure.(a) (b) Usually, we assume that the springs are massless. Therefore, work done is stored in the spring in the form of elastic potential energy of the spring. Thus, potential energy of a spring is the energy associated with the state of compression or expansion of an elastic spring.The potential energy of a spring increases by `15 J` when stretched by 3 cm. If it is stretched by 4 cm, the increase in potential energy
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Principle of Conservation of EnergyTotal energy of an isolated system always remains constant. Since, the universe as a whole may be viewed as an isolated system, total energy of the universe is constant. If one part of the universe loses energy, then other part must gain an equal amount of energy. The principle of conservation of energy cannot be proved as such. However, no violation of this principle has been observed.`U` is the potential energy, K is the kinetic energy and E is the mechanical energy. Which of the following is not possible for a stable
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Three identical spheres of mass M each are placed at the corners of an equilateral triangle of side 2 m. Taking one of the corner as the origin, the position vector of the centre of mass
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A flywheel of moment of inertia `0.4 kg-m^2` and radius `0.2 m` is free to rotate about a central axis. If a string is wrapped around it and it is pulled with a force of 10N, then its angular velocity after `4s` will
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Assertion: When a particle is moving in a straight line with a uniform velocity, its angular momentum is constant. Reason: The angular momentum is non-zero, when particle moves with a uniform
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Centre of Mass The centre of mass of a body or a system of bodies is the point which moves as though all of the mass were concentrated there and all external forces were applied to it. Hence, a point at which the entire mass of the body or system of bodies is supposed to be concentrated is known as the centre of mass. If a system consists of more than one particles (or bodies) and net external force on the system in a particular direction is zero with centre of mass at rest. Then, the centre of mass will
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Centre of Mass The centre of mass of a body or a system of bodies is the point which moves as though all of the mass were concentrated there and all external forces were applied to it. Hence, a point at which the entire mass of the body or system of bodies is supposed to be concentrated is known as the centre of mass. If a system consists of more than one particles (or bodies) and net external force on the system in a particular direction is zero with centre of mass at rest. Then, the centre of mass will
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Cavendish’s ExperimentThe figure shows the schematic drawing of Cavendish’s experiment to determine the value of the gravitational constant. The bar AB has two small lead spheres attached at its ends. The bar is suspended from a rigid support by a fine wire.Two large lead spheres are brought close to the small ones but on opposite sides as shown. The value of G from this experiment came to be `6.67 xx 10^(-11) N-m^2'/'kg^2`.The net torque on the bar
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A particle is moving along a straight line and its position is given by the relation `x=(t^3-6t^2+40)m` Find (a) The time at which velocity is zero. (b) Position and displacement of the particle at that point. (c) Acceleration for the particle at that
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A monkey of mass 40 kg climbs on a rope which can stand a maximum tension 600 N. In which of the following cases will the rope break? The monkey (a) climbs up with an acceleration of 6m/`s^2` (b) climbs down with an acceleration of 4m/`s^2` (c) climbs up with a uniform seed of 5m/s (d) falls down the rope freely under gravity. Take g = 10m/`s^2` and ignore the mass of the
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Calculate the work done when a wire of length l and area of cross – section A is made of material of young’s Modulus Y is stretched by an amount
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Find the work done in breaking a water drop of radius 1 mm into 1000 drops. Given the surface tension of water is `72 × 10^(-3)
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If the volume of block of metal changes by 0.12% when it is heated through `20^oC`. What is the co-efficient of linear expansion of the
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Two conducting slabs of thermal conductivities K1 and K2 are joined as shown in the figure. The temperature of the ends of slab are `θ_1 and θ_2 (θ_1 > θ_2)`. Find the final temperature of
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Two rods A and B are of equal length. Each rod has its ends at temperature T1 and T2 (T1 > T2). What is the condition that will ensure equal rates of flow through the rods A and
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