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answer is v(mg - R/ mg + R)

^{1/2 }please explain how !!_{A}and v_{B}_{ }as shown. The angular velocity of the rod is.$a)20rad/s\phantom{\rule{0ex}{0ex}}b)25rad/s\phantom{\rule{0ex}{0ex}}c)30rad/s\phantom{\rule{0ex}{0ex}}d)50rad/s$

^{2}. The rod is bent in the plane perpendicular to the axis in the middle so that the two halves makes an angle of 60^{0}. the moment of inertia of the bent rod about the same axis would bea)ML

^{2}/48b)ML

^{2}/12c)ML

^{2}/24d)ML

^{2}/8root31) V

2)$\frac{V}{3}$

3)$\frac{2V}{3}$

4)$\frac{3V}{4}$

Answer is 10mr

^{2}please explain how_{0}_{ }rotates freely about a fixed horizontal axis through its centre. A thin cotton pad is fixed on its rim, which can absorb water. The mass of water dripping slowly onto the pad is $\mu $ per second. After what time will the angular velocity of the disc get reduced to half of its initial value.$\left(A\right)\frac{2{m}_{0}}{\mu}\phantom{\rule{0ex}{0ex}}\left(B\right)\frac{3{m}_{0}}{\mu}\phantom{\rule{0ex}{0ex}}\left(C\right)\frac{{m}_{0}}{\mu}\phantom{\rule{0ex}{0ex}}\left(D\right)\frac{{m}_{0}}{2\mu}$

A flywheel at rest is to reach an angular velocity of 24 rad/s in 8 second with constant angular

acceleration. The total angle turned through during this interval is?

options

1-decreseases its mechanical energy 2-its translational kinetic energy

3-rotational ke 4 -pe

Pls answer it quickly

Thank you

A thick hollow sphere has an outer radius of Ro. It rolls down an inclined plane without slipping and its speed at bottom is Vnot. Now the incline waxed so that it is practically frictionless and sphere is observed to slide down. Speed at bottom is 5Vo/4. Radius of gyration of hollow sphere about an axis through its centre is ?

17. A cubical block of side a moving with velocity v on a horizontal smooth the plane as shown in figure. It hits a ridge at point O and starts rotating about the edge in contact with O. The angular speed of the block after it hits O is

$\text{(1)}\frac{\text{3v}}{\text{4a}}\phantom{\rule{0ex}{0ex}}\text{(2)}\frac{\text{3v}}{\text{2a}}\phantom{\rule{0ex}{0ex}}\text{(3)}\sqrt{\frac{3}{2}}\frac{\text{v}}{\text{a}}\phantom{\rule{0ex}{0ex}}\text{(4)Zero}$

Q.15. Starting from rest, a wheel has constant $\alpha $ = 3.0 rad/${s}^{2}$. During a certain 4.0 s interval, it turns through 120 rad. How much time did it take to reach that 4.0 s interval?