Angular Momentum and Law of Conservation of Angular Momentum

Q 1 :
If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be _______ hours 30 minutes. [2024]

0%

(13) $By angular momentum conservation, I_{1} ω_{1} = I_{2} ω_{2}$

$\frac{2}{5} m r^{2} \cdot ω = \frac{2}{5} m {(\frac{3}{4} r)}^{2} \cdot ω^{'} \Rightarrow ω^{'} = \frac{16}{9} ω$

$\frac{2 π}{T^{'}} = \frac{16}{9} \times \frac{2 π}{T} \Rightarrow T^{'} = \frac{9 T}{16} = \frac{9}{16} \times 24 hours = \frac{9 \times 3}{2} hours$

$\Rightarrow T^{'} = \frac{27}{2} hr = 13 h r 30 mins$

Q 2 :
A body of mass 5 kg moving with a uniform speed $3 \sqrt{2} m s^{- 1}$ in X - Y plane along the line $y = x + 4$ . The angular momentum of the particle about the origin will be _____ $k g m^{2}$ $s^{- 1}$ . [2024]

0%

(60) $y - x - 4 = 0$

$d_{1}$ is perpendicular distance of given line from origin.

$d_{1} = | \frac{- 4}{\sqrt{1^{2} + 1^{2}}} | \Rightarrow 2 \sqrt{2} m$

So, $| \vec{L} | = m v d_{1}$

$= 5 \times 3 \sqrt{2} \times 2 \sqrt{2} kg m^{2} / s = 60 kg m^{2} / s$

Q 3 :
Two discs of moment of inertia $I_{1} = 4$ $k g m^{2}$ and $I_{2} = 2$ $k g m^{2}$ about their central axes and normal to their planes, rotating with angular speeds 10 rad/s and 4 rad/s respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is ________ J. [2024]

0%

(24) Here angular momentum will remain conserve

$L = I ω$

$L_{i} = L_{f}$

$4 \times 10 + 2 \times 4 = (6) ω$

$48 = 6 ω$

$ω = 8 rad / \sec$

$Δ K E = K E_{f} - K E_{i}$

$Δ K = \frac{1}{2} (6) {(8)}^{2} - [(\frac{1}{2} 4 \times 10^{2}) + (\frac{1}{2} (2) \times {(4)}^{2})]$

$Δ K = 192 - 216$

$Δ K = - 24 J$

Q 4 :
A uniform rod AB of mass 2 kg and length 30 cm at rest on a smooth horizontal surface. An impulse of force 0.2 Ns is applied to end B. The time taken by the rod to turn through at right angles will be $\frac{π}{x} s$ , where $x =$ _____________ . [2024]

0%

(8)

Topic Question Set

Q 1 :
If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be _______ hours 30 minutes. [2024]

0%

Q 2 :
A body of mass 5 kg moving with a uniform speed $3 \sqrt{2} m s^{- 1}$ in X - Y plane along the line $y = x + 4$ . The angular momentum of the particle about the origin will be _____ $k g m^{2}$ $s^{- 1}$ . [2024]

0%

0%

Q 4 :
A uniform rod AB of mass 2 kg and length 30 cm at rest on a smooth horizontal surface. An impulse of force 0.2 Ns is applied to end B. The time taken by the rod to turn through at right angles will be $\frac{π}{x} s$ , where $x =$ _____________ . [2024]

0%

Want Us to Email you About Special Offers & Updates?

Topic Question Set

Q 1 : If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be _______ hours 30 minutes. [2024]

0%

Q 2 : A body of mass 5 kg moving with a uniform speed 32ms-1 in X - Y plane along the line y=x+4. The angular momentum of the particle about the origin will be _____ kgm2 s-1. [2024]

0%

0%

Q 4 : A uniform rod AB of mass 2 kg and length 30 cm at rest on a smooth horizontal surface. An impulse of force 0.2 Ns is applied to end B. The time taken by the rod to turn through at right angles will be πxs, where x= _____________ . [2024]

0%

Want Us to Email you About Special Offers & Updates?

Q 1 :
If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be _______ hours 30 minutes. [2024]

Q 2 :
A body of mass 5 kg moving with a uniform speed $3 \sqrt{2} m s^{- 1}$ in X - Y plane along the line $y = x + 4$ . The angular momentum of the particle about the origin will be _____ $k g m^{2}$ $s^{- 1}$ . [2024]

Q 4 :
A uniform rod AB of mass 2 kg and length 30 cm at rest on a smooth horizontal surface. An impulse of force 0.2 Ns is applied to end B. The time taken by the rod to turn through at right angles will be $\frac{π}{x} s$ , where $x =$ _____________ . [2024]