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question_answer1) A string is wound around a hollow cylinder of mass 5 kg and radius 0.5m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration (in \[rad/{{s}^{2}}\]) of the cylinder will be (Neglect the mass and thickness of the string):
question_answer2) Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius (in cm) of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is:
question_answer3) A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum (in \[kg\,{{m}^{2}}/s\]) about O will be \[\left( Take\text{ }g=10\text{ }m/{{s}^{2}} \right)\]
question_answer4) A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of a platform of height 5m. When released, it slips off the table in a very short time \[\tau =0.01\text{ }s,\] remaining essentially horizontal. The angle (in radians) by which it would rotate when it hits the ground will be close to:
question_answer5) Moment of inertia of a body about a given axis is\[1.5\text{ }kg\,{{m}^{2}}\]. Initially the body is at rest. In order to produce a rotational kinetic energy of 1200 J, the angular acceleration of \[20\,rad/{{s}^{2}}\] must be applied about the axis for a duration of ____ seconds.
question_answer6) A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of \[\frac{7M}{8}\] and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let \[{{I}_{1}}\] be the moment of inertia of the new sphere about its axis. The ratio \[{{I}_{1}}/{{I}_{2}}\] is\[\frac{140}{x}\]. Find the value of x.
question_answer7) A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque (in Nm) that will make the system rotate about AB at 25 rotations per second in 5s, is close to:
question_answer8) If linear density of a rod of length 3m varies as\[\lambda =2+x,\] then the position of the centre of mass of the rod is \[\frac{P}{7}m\] . Find the value of P.
question_answer9) Two bodies of masses 2 kg and 4 kg are moving with velocities 2 m/s and 10 m/s respectively along the same direction. Then the velocity (in m/s) of their centre of mass will be
question_answer10) A wheel is rotating at 900 r.p.m. about its axis. When the power is cut-off, it comes to rest in 1 minute. The angular retardation in radian/\[{{s}^{2}}\] is\[\frac{\pi }{x}\]. Find the value of x.
question_answer11) A wheel has a speed of 1200 revolutions per minute and is made to slow down at a rate of 4 radian/\[{{s}^{2}}\]. The number of revolutions it makes before coming to rest is
question_answer12) A particle of mass 10 gram is rotating in a plane in circular path of radius 1 m. Its angular momentum is 1 J-sec. The centripetal force (in newton) acting on the particle is
question_answer13) A ring of mass 10 kg and diameter 0.4m is rotated about its axis. If it makes 2100 revolutions per minute, then its angular momentum (in\[kg\,{{m}^{2}}/s\]) will be
question_answer14) X and Y are two loops made from same wire. The radii of X and Y are \[{{r}_{1}}\] and \[{{r}_{2}}\]their M.I. are \[{{I}_{1}}\]and\[{{I}_{2}}\]. If \[{{I}_{2}}/{{I}_{1}}=4\] the value of \[{{r}_{2}}/{{r}_{1}}\] is\[{{\left( K \right)}^{1/3}}\]. Find the value of K.
question_answer15) A particle of mass \[m=5\] units is moving with a uniform speed \[v=3\sqrt{2}\] units in the XOY plane along the straight line \[Y=X+4.\] The magnitude of the angular momentum of the particle about the origin is _______ units.
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The angle (in radians) by which it would rotate when it hits the ground will be close to: 
