System of Particles and Rotational Motion

Two persons of masses 55 kg and 65 kg respectively. are at the opposite ends of the boat. The length of the boat is 3.0 m and weigh 100 kg. The 55 kg man walks to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by

• 3.0 m

• 2.3 m

• zero

• zero

ABC is an equilateral triangle with O as its centre F₁, F₂ and F₃ represent three forces acting on the sides AB, BC and AC respectively. If the total torque about O zero then the magnitude of F₃ is

• F₁ +F₂

• F₁ - F₂

• F₁ +F₂/2

• F₁ +F₂/2

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in the figure. When a string is cut, the initial angular acceleration of the rod is,

• 3g / 2L

• g/L

• 2g/L

• 2g/L

A small object of uniform density rolls up a curved surface with an initial velocity v'. It reaches up to a maximum height of  with respect to the initial position. The object is,

• ring

• solid sphere

• hollow sphere

• hollow sphere

A particle moves in a circle of radius 5 cm with constant speed and time period 0.2 πs. The acceleration of the particle is 

• 25 m/s²

• 36 m/s²

• 5 m/s²

• 5 m/s²

The instantaneous angular position of a point on a rotation wheel is given by the equation 

Q(t)  = 2t³ - 6t²

The torque on the wheel becomes zero at

• t = 0.5 s 

• t = 0.25 s

• t = 2s

• t = 2s

The moment of inertia of a thin uniform rod of mass M  and length L about an axis passing through its mid - point and perpendicular to its length is I_o. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

• I_o + ML²/4

• I_o + 2ML²

• I_o + ML²

• I_o + ML²

A body of mass M hits normally a rigid wall with velocity v and bounces back with the same velocity. The impulse experienced by the body is 

• 1.5 Mv

• 2 Mv

• zero

• zero

An automobile moves on a road with a speed of 54 km h^-1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m² . If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its breaks to the wheel is

• 6.66 kg m²s^-2

• 8.58 kg m²s^-2

• 10.86 kg m²s^-2

• 10.86 kg m²s^-2

• -1

• 2

• zero

• zero