Laws Of Motion

Ten coins are placed one over another as shown.
As the coin has coins on its top, therefore the force experienced by the coin will be . As coin has coin on its top, therefore it will exert a force of on coin.
As every action has equal and opposite reaction therefore coin will give a reaction of to the coin upwards

The coin will experience a reaction force of as it exerts a force of .

Equations of motion are and From Eqs. (i) and (ii), we get Substituting the value of in E we get

Suppose the block will leave the sphere at point ,
which is at a distance from the sphere

When block leaves the sphere at point , the normal reaction becomes zero


From figure

and

Central attractive force



or

Here, Mass of the particle,
(minus sign for direction of force)
Acceleration,
The position of the body at any time t is given by

The position of the body at is therefore

Position of the body at
Here,

Since the applied force is greater than
therefore the block will be in motion
so, we should consider
or
This would cause acceleration of
block acceleration

Acceleration of block

Consider the following figures:

We know that for a body moving with constant acceleration, the kinematics equation is given as .
Initial velocity,



Now for smooth inclined plane
For rough inclined plane
Also, time taken to travel down the smooth inclined plane and time taken to travel down the rough inclined plane
Therefore,






Now we know
Therefore,

Let acceleration of system (rope + block) is an along the direction of applied force. Then Draw the FBD of block and rope as shown in figure.where, is the required parameter For block

When friction is absent

...(i)
Whrn friction is present


...(ii)
From Eqs. (i) and (ii)
or
or

or
or or

Since, we know that from a position-time graph of a body

Given, mass of the ball, ,
and the time taken the man to throw a ball,

Change in momentum of the ball,

Since, we know,
Force = Rate of change in linear momentum
(Putting values)