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A solid disc and a ring, both of radius 10 cm are placed on a horizontal table simultaneously, with initial angular speed equal to 10 π rad `(s^-1)`. Which of the two will start to roll earlier ? The co-efficient of kinetic friction is `µ_k =
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A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination 30°. The coefficient of static friction `µ_s` = 0.25. (a) How much is the force of friction acting on the cylinder ? (b) What is the work done against friction during rolling ? (c) If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly
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Read each statement below carefully, and state, with reasons, if it is true or false;(a) During rolling, the force of friction acts in the same direction as the direction of motion of the CM of the body. (b) The instantaneous speed of the point of contact during rolling is zero. (c) The instantaneous acceleration of the point of contact during rolling is zero. (d) For perfect rolling motion, work done against friction is zero. (e) A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling)
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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : Show `p=p'_1+m_iV` where pi is the momentum of the ith particle (of mass `m_i`) and `p′_i = m_iv′_i`. Note `v′_i` is the velocity of the ith
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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : Show K=K'+1/2M`V^2` where K is the total kinetic energy of the system of particles, K′ is the total kinetic energy of the system when the particle
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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : Show where `L'=r'_1xxp'_1` is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember `r'1=r_1-R`;
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Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : Show `(dL')/(dt)=sum r'_1xx(dp')/(dt)` Further, show that `(dL')/(dt)=τ'_(ext)` where `τ'_(ext)` is the sum of all external torques acting on the system about the centre of mass. (Hint
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.Is 243 a perfect
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Is 392 a perfect cube? If not, find the smallest natural number by which 392 must be multiplied so that the product is a perfect
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Is 53240 a perfect cube? If not, then by which smallest natural number should 53240 be divided so that the quotient is a perfect
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Is 1188 a perfect cube? If not, by which smallest natural number should 1188 be divided so that the quotient is a perfect
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Is 68600 a perfect cube? If not, find the smallest number by which 68600 must be multiplied to get a perfect
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Which of the following numbers are not perfect cubes?(i) 216 (ii) 128 (iii) 1000 (iv) 100 (v)
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Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. 243
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Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. 256
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Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. 72
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Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.
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Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.
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Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. 81
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Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. 128
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