Work and Kinetic Energy

Q. A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as a flywheel. If it rotates at 600 rpm, the kinetic energy of the flywheel, in joules is

1. 395
2. 790
3. 1580
4. 3160

Q. An annular disc has a mass m, inner radius R and outer radius 2 R. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is

1. $\frac{9}{16}m{v}^2$
2. $\frac{11}{16}m{v}^2$
3. $\frac{13}{16}m{v}^2$
4. $\frac{15}{16}m{v}^2$

Q. An ideal spring with spring constant k is hung from a ceiling and a block of mass M is attached to its lower end. If the mass is released with the spring initially unstretched, the maximum extension in the spring is

1. $\frac{4Mg}{k}$
2. $\frac{2Mg}{k}$
3. $\frac{Mg}{k}$
4. $\frac{Mg}{2k}$

Q. A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $r\left(t\right)=t^2,\theta \left(t\right)=t,$ where t is time. The kinetic energy of the particle at time t= 2 is

1. 4
2. 12
3. 16
4. 24

Q. A block of mass m is released at rest from a point P of a rough circular path of radius r as shown in the figure. There is a spring of stiffness k at the other end of the path. (acceleration due to gravity = g)
The maximum spring deflection is

1. $\text{independent of}r$
2. $\text{more than}\sqrt{2mgr/k}$
3. $\text{equal to}\sqrt{2mgr/k}$
4. $\text{less than}\sqrt{2mgr/k}$

Q. A particle enters into a smooth frictionless circular loop of radius R, at point P as shown below. If g is the acceleration due gravity, then the minimum speed with which the particle should enter the circular loop such it can complete one full circular revolution is

1. $\sqrt{5Rg}$
2. $\sqrt{3Rg}$
3. $\sqrt{2Rg}$
4. $\infty$