When a block is placed on a wedge as shown in the figure, the block starts sliding down and the wedge also start sliding on ground. All surfaces are rough. The centre of mass of (Wedge + block) system will move :
Friction force between wedge and block is internal i.e. will not change motion of centre of mass. Friction force on the wedge by ground is external and causes centre of mass to move towards right. Gravitational force (mg) on block brings it downward hence centre of mass comes down.
The correct answer is: rightward and downward
Assuming potential energy U at ground level to be zero.
All objects are made up of same material
UP = Potential energy of solid sphere
UQ = Potential energy of solid cube
UR = Potential energy of solid cone
US = Potential energy of solid cylinder
centre of mass of cone is on smallest height.
The correct answers are: US > UP, UQ >US, US > UR
Two particles A and B start moving due to their mutual interaction only. If any time t, are their respective acceleration, are their respective velocities and upto that time WA and WB are the work done on A and B respectively by the mutual force, mA and mB are their masses respectively, then which of the following is always incorrect.
Since ∴ Momentum of system will remain conserved, equal to zero.
The correct answers are:
The diagram shows the velocity-time graph for two masses R and S that collided elastically. Which of the following statement is true?
(i) Since, both have positive final velocities, hence, both moved in the same direction after collision.
(ii) at t = 2 sec. both had equal velocities.
(iii) by conservation of linear momentum, we can say that mass of R was greater than mass of S.
The correct answers are: R and S moved in the same direction after the collision, The velocities of R and S were equal at the mid time of the collision, The mass of R was greater than mass of S
A particle strikes a horizontal smooth floor with a velocity u making an angle with the floor and rebounds with velocity v making and angle with the floor. If the coefficient of restitution between the particle and the floor is e, then :
In horizontal direction, momentum is conserved :
in vertical direction,
The correct answers are: the impulse delivered by the floor to the body is the ratio of the final kinetic energy to the initial kinetic energy is
A bag of mass M hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined system (bag + bullet) which of the following are correct
Since, Fext = 0
Hence, momentum will remain conserved equal to mv.
and final kinetic energy is
The correct answers are: Momentum is mv, KE is m2v2(M + m)/2
A ball of mass m moving with a velocity v hits a massive wall of mass M (M >> m) moving towards the ball with a velocity u. An elastic impact lasts for a time Δt. Which of the following are correct.
In an elastic collision
vsep = vapp
change in momentum of ball is
= 2m(u + v)
The correct answers are: The average elastic force acting on the ball is The kinetic energy of the ball increase by 2mu(u+v)
Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure.
The acceleration of the centre of mass is
The displacement of the centre of mass at time t will be
Therefore initial velocity is either in direction of constant force or opposite to it. Hence the particle will move in straight line and speed may increase or decrease. When F and u are antiparallel then particle will come to rest for an instant and will return back.
Initial velocity is perpendicular to constant force, hence the path will be parabolic with speed of particle increasing. means instantaneous velocity is always perpendicular to force. Hence the speed will remain constant. And also constant. Since the particle moves in one plane, the resulting motion has to be circular. Hence initial velocity is in same direction of constant acceleration, therefore, particle moves in straight line with increasing speed.
The correct answers are: The displacement of the centre of mass at time t is The displacement of the right block, if the extension of the spring is x0 at time t, is The displacement of the left block, if the extension of the spring is x0 at time t, is
For a two-body system in absence of external forces, the kinetic energy as measured from ground frame is K0 and from centre of mass frame is Kcm. Pick up the correct statement.
It can be shown that
where M is the total mass of the system and Vcm is velocity of centre of mass with respect to ground.
Due to internal changes Kcm can change but Vcm will remain same. Hence only Kcm portion of kinetic energy can be transformed to some other from of energy.
The correct answers are: The kinetic energy as measured from centre of mass frame is least, Only the portion of energy Kcm can be transformed from one form to another due to internal changes in the system., The system always retains at least K0–Kcm amount of kinetic energy as measured from ground frame irrespective of any kind of internal change in the system.
A smooth sphere A of mass m collides elastically with an identical sphere B at rest. The velocity of A before collision is 8 m/s in a direction making 60° with the line joining the centre at the time of impact. Which of the following is/are possible :
Sphere A moving with velocity v has a component v/2 along the line joining the centres of the spheres at the time of collision and another component perpendicular to the previous direction. After collision the component along the line will interchange i.e. B will move with v/2 velocity i.e., 4 m/s along the line joining the centres and A moves with velocity at perpendicular direction to B.
The correct answers are: the direction of motion of A and B after collision are at right angles, the speed of B after collision is 4 m/s