a) In a lab frame of reference,

Velocity of center of mass is given by,

v'=(mv_OA+ mv_OB)/2m

Now, in center of mass frame of reference,

Since, there will be perfectly elastic collision. After collision, they exchange their velocity.

In lab frame of reference,

Deceleration due to the friction =µg

From kinematics we have,

V_F=V_B-µgt

Since the final velocity of B is zero, we get t=10s.

Distance travelled d is given by,

d = V_Bt - (µgt²)/2

Inserting given values, the distance travelled by block is 50m.

b)...

Here, Ma=Mg-T

or, M(g/8)=Mg-T

or, T= M(g-g/8)

or, T= 7Mg/8

so, work done = T*d cos180⁰

=7Mg/8 * (-d)

= -7Mgd/8

So, correct option is d

The change in magnitude of the ball is 28 kgm/s.

Solution:

Here,

mass of the ball (m) = 2kg

initial velocity of the ball (u) = 8 m/s (say downward direction is positive)

final velocity of the ball (v) = -6 m/s (because in upward direction)

Hence,

change in linear momentum of the ball (delta P) = m(v-u)

= 2 (-6 - 8)

= 2 (-14)

= -28 kgm/s

The magnitude of change in linear momentum of the ball is 28 kgm/s.

Work done is equal to Force (acting in the direction of displacement) times the displacement i.e. W=F.S where (.) is dot product.For the work done we need component of force along the direction of displacement but displacement and force are 90, at each and every point on the circular track and therefore the component of force along the direction of displacement will always be zero in case of a body moving in a circular track or a body performing circular motion. We know W=F.S or F.Scos(θ),...

The energy is dissipated in the form of heat. The heat energy so produced is not available for work.

There is no external force as car is having constant speed

The energy of the bus has to go somewhere, and the momentum too, as they are independently conserved.

The meteorite moves under the force of gravity therefore , its momentum goes on changing . But total momentum of meteorite and earth is always conserved

Since the protons are positively charged particles, they will repal each other. To bring them nearer, work has to be done against the force of repulsion and this will be stored up in the system as potential energy. So the potential energy of the system will increase.

While inflating the rubber tube of a bicycle, a piston moves in a barrel There exists a friction between the barrel and the piston as the piston moves in the barrel. Some work is to be done against the friction. This work done against the friction is converted in to the heat which heats up the pump.