Questions by varun

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A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop

asked Mar 19, 2022 in 11th Physics

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The oxygen molecule has a mass of `5.30 × 10^(-26)` kg and a moment of inertia of `1.94×10^(-46)` kg `m^2` about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the

asked Mar 19, 2022 in 11th Physics

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A solid cylinder rolls up an inclined plane of angle of inclination 30°. At the bottom of the inclined plane the centre of mass of the cylinder has a speed of 5 m/s. (a) How far will the cylinder go up the plane? (b) How long will it take to return to the

asked Mar 19, 2022 in 11th Physics

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As shown in Fig., the two sides of a step ladder BA and CA are 1.6 m long and hinged at A. A rope DE, 0.5 m is tied half way up. A weight 40 kg is suspended from a point F, 1.2 m from B along the ladder BA. Assuming the floor to be friction-less and neglecting the weight of the ladder, find the tension in the rope and forces exerted by the floor on the ladder. (Take g = 9.8 m/`s^2`) (Hint: Consider the equilibrium of each side of the ladder separately.)

asked Mar 19, 2022 in 11th Physics

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A man stands on a rotating platform, with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90cm to 20cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg `m^2`. (a) What is his new angular speed? (Neglect friction.) (b) Is kinetic energy conserved in the process? If not, from where does

asked Mar 19, 2022 in 11th Physics

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A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it. (Hint: The moment of inertia of the door about the vertical axis at one end is

asked Mar 19, 2022 in 11th Physics

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Two discs of moments of inertia `I_1` and `I_2` about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds `ω_1` and `ω_2` are brought into contact face to face with their axes of rotation coincident. (a) What is the angular speed of the two-disc system? (b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs. How do you account for this loss in energy? Take `ω_1` ≠

asked Mar 19, 2022 in 11th Physics

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(a) Prove the theorem of perpendicular axes. (Hint : Square of the distance of a point (x, y) in the x–y plane from an axis through the origin and perpendicular to the plane is `x^2+y^2`). (b) Prove the theorem of parallel axes. (Hint : If the centre of mass is chosen to be the origin `m_ir_i = 0`

asked Mar 19, 2022 in 11th Physics

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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

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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

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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

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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

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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

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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

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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

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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

asked Mar 19, 2022 in 11th Physics

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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

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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

asked Mar 19, 2022 in 11th Physics

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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

asked Mar 19, 2022 in 11th Physics

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

asked Mar 19, 2022 in 11th Physics

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