A thin circular ring of mass $m$ and radius $R$ is rotating bout its axis with a constant angular velocity $\omega$. Two objects each of mass $M$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $\omega '$ =
$\frac{{\omega \left( {m + 2M} \right)}}{m}$
$\frac{{\omega \left( {m - 2M} \right)}}{{\left( {m + 2M} \right)}}$
$\frac{{\omega m}}{{(m + M)}}$
$\frac{{\omega m}}{{\left( {m + 2M} \right)}}$
A constant torque acting on a uniform circular wheel changes its angular momentum from $L_0$ to $4L_0$ in $4\,s$ . The magnitude of this torque is
$A$ car travelling on a smooth road passes through $a$ curved portion of the road in form of an arc of circle of radius $10 m$. If the mass of car is $500\, kg$, the reaction on car at lowest point $P$ where its speed is $20 m/s$ is ......... $kN$.
Three bodies , a ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity?
A thin rod of mass $m$ and length $l$ is oscillating about horizontal axis through its one end. Its maximum angular speed is $\omega $. Its centre of mass will rise upto maximum height
When helical gear $M$ turns as shown, gears $I$ & $H$ turn in the following manner. Which of the following is correct ? (Assuming no slipping anywhere)