A bead of mass $displaystylefrac12kg$ starts from rest from A to move in a vertical place along a smooth fixed quarter ring of radius $displaystyle5m$, under the action of a constant horizontal force $displaystylef=5N$ as shown. The speed of bead as it reaches the point (B) is [Take $displaystyleg=10m{s}^{-2}]$

In a carbon monoxide molecule, the carbon and the oxygen atoms are separated by a distance $1.2\times {10}^{-10}m$. The distance of the centre of mass from the carbon atom is

A mass 'm' is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall or release?

A pump motor is used to deliver water at a certain rate from a given pipe. To obtain 'n' times water from the same pipe in the same time by what amount (a) the force and (b) power of the motor should be increased ?

A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of ${45}^{\circ }$ with the initial vertical direction is

A spring of spring constant $5\times {10}^{3}N/m$ is stretched initially by 5 cm from the unstretched position. The work required to further stretch the spring by another 5 cm is .

A marble block of mass 2 kg lying on ice when given a velocity of $6m/s$ is stopped by friction in 10s. Then the coefficient of friction is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency $\omega .$ The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

System shown in figure is released from rest . Pulley and spring is mass less and friction is absent everywhere. The speed of $5kg$ block when $2kg$ block leaves the constant of with ground is (force constant of spring $k=40N/m\text{and}g=10m/s^2)$

Block $A$ is hanging from vertical spring of spring constant $K$ and is rest. Block $B$ strikes block $A$ with velocity $v$ and sticks to it. Then the value of $v$ for which the spring just attains natural length is