A disc of mass m and radius R is placed over a plank of mass m. There is sufficient friction between disc and plank to prevent slipping and there is no friction between plank and ground. A horizontal force F is applied at the centre of the disc, then

A uniform disc of radius 20 cm and mass 2 kg can rotate about a fixed axis through the centre and perpendicular to its plane. A massless cord is round along the rim of the disc. If a uniform force of2 newtons is applied on the cord, tangential acceleration of a point on the rim of the disc will be :-

A uniform disc of mass  m  and radius  R  starts with velocity  V0  on a rough horizontal floor with a purely sliding motion at  t  =  0 . At  t  =  t0 , disc starts rolling without sliding: (Assume coefficient of kinetic friction  μ  )

A solid cylinder of mass m is placed over a plank of same mass as shown in figure. The plank is placed on smooth horizontal surface. There is sufficient friction between cylinder and plank to prevent slipping. If a force is applied at the centre of the cylinder then find the ratio of magnitude of acceleration of cylinder to magnitude of the acceleration of the plank.

force ‘F’ is applied at the top of a ring of mass ‘M’ and radius ‘R’ placed on a rough horizontal surface as shown in the figure. Friction is sufficient to prevent slipping. The friction force acting on the ring is

A disc placed on a frictionless horizontal plank is rotating with a constant angualr velocity ( vec{omega} ) about its vertical axis. Now the plank is made to move with a constant acceleration ( vec{a} ) on a straight path. Initially the centre of the disc is at the origin of ( x y z ) space which is fixed with the plank and ( x y ) plane is on the plank. List-I gives some possible ( vec{a}, vec{omega} ) and List-II gives trajectories of instantaneous centre of rotation of the disc. begin{tabular}{|c|l|c|l|} hline multicolumn{2}{|c|}{ List ( -mathrm{I} )} & multicolumn{2}{|c|}{ List -II } hline (I) & ( overrightarrow{mathrm{a}}=-2 hat{mathrm{j}} mathrm{m} / mathrm{s}^{2}, vec{omega}=4 hat{mathrm{k}} mathrm{rad} / mathrm{s} ) & ( (P) ) & ( mathrm{y}=4 ) hline (II) & ( overrightarrow{mathrm{a}}=-2 hat{mathrm{j}} mathrm{m} / mathrm{s}^{2}, vec{omega}=-4 hat{mathrm{k}} mathrm{rad} / mathrm{s} ) & ( (mathrm{Q}) ) & ( mathrm{y}=4 mathrm{x}^{2}(mathrm{x} leq 0) ) hline (III) & ( overrightarrow{mathrm{a}}=-2 hat{mathrm{i}} mathrm{m} / mathrm{s}^{2}, vec{omega}=4 hat{mathrm{k}} mathrm{rad} / mathrm{s} ) & ( (mathrm{R}) ) & ( mathrm{y}=4 mathrm{x}^{2}(mathrm{x} geq 0) ) hline (IV) & ( overrightarrow{mathrm{a}}=-2 hat{mathrm{i}} mathrm{m} / mathrm{s}^{2}, vec{omega}=-4 hat{mathrm{k}} mathrm{rad} / mathrm{s} ) & ( (mathrm{S}) ) & ( mathrm{x}=4 mathrm{y}^{2}(mathrm{y} geq 0) ) hline & multicolumn{2}{|c|}{( (T) )} & ( mathrm{x}=4 mathrm{y}^{2}(mathrm{y} leq 0) ) hline end{tabular} Which one of the following options is correct? (A) I ( rightarrow mathrm{P} ), II ( rightarrow mathrm{Q} ), III ( rightarrow mathrm{T} ), IV ( rightarrow mathrm{S} ) (B) I ( rightarrow ) Q, II ( rightarrow ) R, III ( rightarrow ) S, IV ( rightarrow ) T (C) I ( rightarrow ) Q, II ( rightarrow ) S, III ( rightarrow ) T, IV ( rightarrow ) R (D) I ( rightarrow ) R, II ( rightarrow ) Q, III ( rightarrow ) S, IV ( rightarrow ) T