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CBSE - Class 11 > Physics > System of Particles and Rotational Motion Worksheets

Free CBSE - Class 11 Physics - System of Particles and Rotational Motion worksheets

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1.
Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : (a) Show $p_i = p'_i + m_i V$ where $p_i$ is the momentum of the ith particle (of mass $m_i$) and $p'_i = m_i v'_i$. Note $v'_i$ is the velocity of the ith particle relative to the centre of mass. Also, prove using the definition of the centre of mass $\sum p'_i = 0$.
2.
Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : (b) Show $K = K' + \frac{MV^2}{2}$ where $K$ is the total kinetic energy of the system of particles, $K'$ is the total kinetic energy of the system when the particle velocities are taken with respect to the centre of mass and $\frac{MV^2}{2}$ is the kinetic energy of the translation of the system as a whole (i.e. of the centre of mass motion of the system). The result has been used in Sec. 7.14.
3.
Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : (c) Show $L = L' + R \times MV$ where $L' = \sum r'_i \times p'_i$ is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember $r'_i = r_i - R$; rest of the notation is the standard notation used in the chapter. Note $L'$ and $M \times R V$ can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles.
4.
Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : (d) Show $\frac{d L'}{dt} = \sum r'_i \times \frac{dp'_i}{dt}$ Further, show that $\frac{d L'}{dt} = \tau'_{ext}$ where $\tau'_{ext}$ is the sum of all external torques acting on the system about the centre of mass. (Hint : Use the definition of centre of mass and third law of motion. Assume the internal forces between any two particles act along the line joining the particles.)
5.
A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination $30^o$. The co-efficient of static friction $\mu_s = 0.25$. (c) If the inclination $\theta$ of the plane is increased, at what value of $\theta$ does the cylinder begin to skid, and not roll perfectly ?
6.
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.
7.
Read each statement below carefully, and state, with reasons, if it is true or false; (b) The instantaneous speed of the point of contact during rolling is zero.
8.
Read each statement below carefully, and state, with reasons, if it is true or false; (c) The instantaneous acceleration of the point of contact during rolling is zero.
9.
Read each statement below carefully, and state, with reasons, if it is true or false; (d) For perfect rolling motion, work done against friction is zero.
10.
Read each statement below carefully, and state, with reasons, if it is true or false; (e) A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling) motion.
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