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Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by `v^2=(2gh)/(1+k^2/R^2)` using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A disc rotating about its axis with angular speed `ω_o` is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the disc shown in Fig. ? Will the disc roll in the direction indicated ?

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Explain why friction is necessary to make the disc in Fig. roll in the direction indicated. (a) Give the direction of frictional force at B, and the sense of frictional torque, before perfect rolling begins. (b) What is the force of friction after perfect rolling begins

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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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 =

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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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

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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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)

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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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

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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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`;

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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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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The displacement of a particle is represented by the equation `y = 3 cos (pi/ 4 - ωt)` . The motion of the particle

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The displacement of a particle is represented by the equation `y = sin^3 ωt` . The motion

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The relation between acceleration and displacement of four particles are given

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Motion of an oscillating liquid column in a U-tube

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A particle is acted simultaneously by mutually perpendicular simple hormonic motions `x = a cos ωt and y = a sin ωt` . The trajectory of motion of the particle will

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The displacement of a particle varies with time according to the relation `y = a sin ωt + b cos

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Four pendulums A, B, C and D are suspended from the same elastic support as shown in Fig. . A and C are of the same length, while B is smaller than A and D is larger than A. If A is given a transverse

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Fig. shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P

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The equation of motion of a particle is `x = a cos (α t )^ 2` . The motion

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A particle executing S.H.M. has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2 . The period of oscillation

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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