Rigid Body Dynamics MSQ - Physics MCQ

The acceleration of three sections of rope 1, 2, 3 are as shown.

Hence for the section of rope in contact with pulley, acceleration increases till the section looses contact with pulley.

Due to friction between string and pulley, the tension in right portion of string is larger in comparison to tension in the left portion of string.

The correct answers are: Magnitude of force exerted by string on mass m₂ is larger as compared to that exerted by string on mass  m₁., The acceleration of small length dℓ of string in contact with block of mass m₂ remains constant.

As  Angular momentum, conserved. F = 0, linear momentum will remain compound.

As the two balls will move radially out, I changes. In order to keep the angular momentum  conserved, angular speed (ω) should change.

The correct answers are: Angular momentum, Linear momentum, Kinetic energy

Let m and M be mass of man and ladder. From FBD normal reaction at A is N₁ = (m + M)g which remains constant. Net torque on man + ladder is zero about B. If x decreases then torque of m about B will decrease.

Hence f must increases.

The correct answers are: Magnitude of normal reaction by wall on ladder at point B will increase., Magnitude of normal reaction by floor on ladder at point A will remain unchanged, Magnitude of friction force by floor on ladder at point A will increase

As the disc is in combined rotation and translation, each point has a tangential velocity and a linear velocity in the forward direction.

From figure

v_net (for lower point) = 

and Acceleration 

(Since linear speed is constant

The correct answers are: Velocity is zero, acceleration is v²/R

The ball has v', component of its velocity perpendicular to the length of rod immediately after the collision. u is velocity of COM of the rod and is angular velocity of the rod, just after collision. The ball strikes the rod with speed v cos 53° in perpendicular direction and its component along the length of the rod after the collision is unchanged

using for the point of collision.

Velocity of separation = Velocity of approach

Conserving linear momentum (of rod + particle), in the direction ⊥ to the rod.

Conserving angular moment about point ‘D’ as shown in the figure

In the same time, distance travelled 

Using angular impulse-angular momentum equation.

The correct answers are: The angular velocity of the rod will be  The centre of the rod will travel a distance  in the time in which it makes half rotation, Impulse of the impact force is 

All points in the body in plane perpendicular to the axis of rotation revolve in concentric circles. All points lying on circle of same radius have same speed (and also same magnitude of acceleration) but different directions of velocity (also different directions of acceleration)

Hence there cannot be two points in the given plane with same velocity or with same acceleration.

As mentioned above, points lying on circle of same radius have same speed.

Angular speed of body at any instant w.r.t. any point on body is same by definition.

The correct answers are: Speed of all the particles lying on the curved surface of a cylinder whose axis coincides with the axis of rotation is same., Angular speed of the body is same as seen from any point in the body

By FBD of particular
mg – T = ma
10 – T = a

BY FBD of disc

By equation (1) and (2)
a = 5 m/s²
and T = 5 N

For angular displacement of disc

Work done by torque 

K₂ – K₁ = 200J

The correct answers are: the tension in the cord is 5 N, in first 4 seconds the angular displacement of the disc is 40 rad., the work done by the torque on the disc in first 4 sec. is 200 J, the increase in the kinetic energy of the disc in the first 4 seconds is 200 J

(i) Conserving linear momentum

–2mv + 2v.m = 0 = MB_cm
V_cm = 0
(ii) As ball stick to Rod
Conserving angular momentum about O

As the normal force exerted by horizontal surface passes through point B, external torque on the ball is zero about point B. So angular momentum of ball is conserved about point B 

The correct answers are: point A, point C

The correct answers are: Angular acceleration is 2.5 rad/s², Acceleration of B is 2.5 m/s²