11.

Two masses 10 kg and 20 kg respectively are connected by a massless springs as shown in the figure. A force of 200 N acts on the 20 kg mass. At the instant shown is a figure the 10 kg mass has an acceleration of 12 m/s2. The value of the acceleration of 20 kg mass is

• 4 m/s²

• 10 m/s²

• 20 m/s²

• 30 m/s²

A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping throuhgout these motions). The directions of the frictional force acting on the cylinder are

• Up the incline, while ascending and down the incline while descending

• Up the incline, while ascending as well as descending

• down the incline, while ascending and up the incline while descending

• Down the incline while ascending as well as descending.

A long block A of mass M is at rest on a smooth horizontal surface.  A small block B of mass M/2 is placed on A at one end and projected along A with same velocity v. The coefficient of friction between the block is μ. Then the acceleration of blocks A and B before reaching a common velocity will be respectively

• $\frac{\mathrm{\mu g}}{2} (\mathrm{towards} \mathrm{right}), \frac{\mathrm{\mu g}}{2} (\mathrm{towards} \mathrm{left})$

• $\mathrm{\mu g} (\mathrm{towards} \mathrm{right}), \mathrm{\mu g} (\mathrm{towards} \mathrm{left})$

• $\frac{\mathrm{ug}}{2} (\mathrm{towards} \mathrm{right}), \mathrm{\mu g} (\mathrm{towards} \mathrm{left})$

• $\mathrm{\mu g} (\mathrm{towards} \mathrm{right}), \frac{\mathrm{\mu g}}{2} (\mathrm{towards} \mathrm{left})$

A uniform rod of length l is free to rotate in a vertical plane about a fixed horizontal axis through B. The rod begins rotating from rest from its unstable equilibrium position. When, it has turned through an angle θ, its angular velocity ω is given by

• $\sqrt{\left(\frac{6\mathrm{g}}{\mathrm{I}}\right)} \sin \frac{\mathrm{\theta }}{2}$

• $\sqrt{\left(\frac{6\mathrm{g}}{\mathrm{I}}\right)} \cos \frac{\mathrm{\theta }}{2}$

• $\sqrt{\left(\frac{6\mathrm{g}}{\mathrm{I}}\right)} \sin \mathrm{\theta }$

• $\sqrt{\left(\frac{6\mathrm{g}}{\mathrm{l}}\right)} \cos \mathrm{\theta }$

A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in any way. A ball of mass m moving with speed V collides elastically with the stick as shown in fig below. If after the collision, the ball comes to rest, then what should be the mass of the ball?

• m = 2M

• m = M

• m= M/2

• m = M/A

ABC is the right-angled triangular plane of uniform thickness. The sides are such that AB>BC as shown in the figure. I₁, I₂, I₃ are moments of inertia about AB, BC and AC, respectively. Then which of the following relations is correct?

• I₁ = I₂ = I₃

• I₂ > I₁> I₃

• I₃<I₂<1₁

• I₃>I₁>I₂

An ice-berg of density 900 kgm^-3 is floating in the water of density 1000 kgm^-3. The percentage of the volume of ice-berg outside the water is

• 20%

• 35%

• 10%

• 11%

A solid cylinder is attached to a horizontal massless spring as shown in the figure. If the cylinder rolls without slipping, the time period of oscillation of the cylinder is

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{x}}{\mathrm{g}}}$

• $2\mathrm{\pi }\sqrt{\frac{2\mathrm{M}}{3\mathrm{K}}}$

• $2\mathrm{\pi }\sqrt{\frac{3\mathrm{M}}{8\mathrm{K}}}$

• $2\mathrm{\pi }\sqrt{\frac{3\mathrm{M}}{2\mathrm{K}}}$

A particular of mass m is executing oscillation about the origin on X- axis. Its potential energy is V(x) = K |x|³. Where K is a positive constant. If the amplitude of oscillation is a, then its time period T is proportional to

• $\frac{1}{\sqrt{a}}$

• a

• $\sqrt{a}$

• a^3/2

A steam of a liquid of density ρ flowing horizontally with speed v rushes out of a tube of radius r and hits a vertical wall nearly normally. Assuming that the liquid does not rebound from the wall, the force exerted on the wall by the impact of the liquid is given by

• πrρv

• πrρv²

• πr²ρv

• πr²ρv²