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Physics System of Particles and Rotational Motion

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Physics System of Particles and Rotational Motion Class 11th

A block of mass $2 m$ is moving with speed $v$ towards a spring block system as shown in the figure. if collision of the two blocks is perfectly inelastic then maximum compression in the spring will be

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alok kumar singh

Contributor-Level 10

Applying conservation of momentum for collision of blocks

$2 m v + 0 = 3 m v^{'}$

$? v^{'} = \frac{2 v}{3} \dots (1)$

Now, from conservation of energy

$\frac{1}{2} * 3 m * {v^{'}}^{2} = \frac{1}{2} k x_{0}^{2}$

$x_{0} = \sqrt[]{\frac{3 m v^{' 2}}{k}} = v' \sqrt[]{\frac{3 m}{k}}$

$= \frac{2 v}{3} \sqrt[]{\frac{3 m}{k}} = v \sqrt[]{\frac{4 m}{3 k}}$

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New answer posted

a month ago

Physics System of Particles and Rotational Motion Class 11th

Moment of inertia of a system made from three uniform rods each of mass m and length l joined to each other, as shown in the figure about one end O and perpendicular to its plane will be

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Raj Pandey

Contributor-Level 9

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New answer posted

a month ago

Physics System of Particles and Rotational Motion Class 11th

A body crosses the topmost point of a vertical circle with critical speed. Its centripetal acceleration, when the string is horizontal will be

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Raj Pandey

Contributor-Level 9

$a_{cp} = \frac{v^{2}}{r} = \frac{{(\sqrt[]{3 g l})}^{2}}{l} = \frac{3 g l}{l} = 3 g$

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New answer posted

a month ago

Physics System of Particles and Rotational Motion Class 11th

A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity $σ$ ). Its kinetic energy is

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Raj Pandey

Contributor-Level 9

Kinetic energy $= \frac{1}{2} I ω^{2}$ , and for ring $I = m r^{2}$

Hence $K E = \frac{1}{2} m r^{2} ω^{2}$

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a month ago

Physics System of Particles and Rotational Motion Class 11th

Two circular rings (of same material) are of same thickness. The diameter of first ring is twice that of second. The moment of inertia of first ring as compared to that of second is

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Vishal Baghel

Contributor-Level 10

$\frac{l_{1}}{l_{2}} = \frac{M_{1} R_{1}^{2}}{M_{2} R_{2}^{2}} = \frac{ρ * 2 π R_{1} * R_{1}^{2}}{ρ * 2 π R_{2} * R_{2}^{2}} = \frac{R_{1}^{3}}{R_{2}^{3}} = \frac{8}{1}$

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New answer posted

a month ago

Physics System of Particles and Rotational Motion Class 11th

In rotational motion of a rigid body about an axis, particles move with

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Vishal Baghel

Contributor-Level 10

In rotational motion, angular velocity of every particle on rigid body will be same. But linear velocity is given as v = $r ω .$

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New answer posted

a month ago

Physics System of Particles and Rotational Motion Class 11th

A body of moment of inertia 4 kg m2 rotating with an angular speed of 4 rad/s has the 4x J of kinetic energy. Determine the value of x.

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Vishal Baghel

Contributor-Level 10

$K . E = \frac{1}{2} l ω^{2}$

$K . E = \frac{1}{2} * 4 * 16 = 32 = 4 * 8 J$

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New answer posted

a month ago

Physics System of Particles and Rotational Motion Class 11th

. An automobile engine develops 10⁵ W power when rotating at an angular speed of 900 rad/minute. The instantaneous torque delivered by the engine is

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alok kumar singh

Contributor-Level 10

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New answer posted

a month ago

Physics System of Particles and Rotational Motion Class 11th

A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertial about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance 'h', the square of angular velocity of wheel will be:

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alok kumar singh

Contributor-Level 10

mg – T = ma . (1)

T * R = l a . (2)

a = a R . (3)

With the help of equations (1), (2) and (3), we get

-> $a = \frac{m g}{m + \frac{l}{R^{2}}}$

$v = \sqrt[]{2 a h} = ω R$

$\Rightarrow ω^{2} = \frac{2 m g h}{l + m R^{2}}$

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New answer posted

a month ago

Physics System of Particles and Rotational Motion Class 11th

The momentum of inertia of a uniform thin rod about a perpendicular axis passing through on end is I1. The same rod is into a ring and its moment of inertia about a diameter is I2. If $\frac{I_{1}}{I_{2}} i s \frac{X π^{2}}{3},$ $\frac{_{}}{_{}} \frac{^{}}{}$ then the value of x will be__________.

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Vishal Baghel

Contributor-Level 10

According to question, we can write

$l = 2 π r \Rightarrow r = \frac{l}{2 π}$

$I_{1} = \frac{m l^{2}}{3}, a n d I_{2} = \frac{m r^{2}}{2} = \frac{m l^{2}}{8 π^{2}}$

$\Rightarrow \frac{I_{1}}{I_{2}} = \frac{m l^{2}}{3} * \frac{8 π^{2}}{m l^{2}} = \frac{8 π^{2}}{3}$

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