Laws Of Motion

Step 1: Concept
Conservation of Linear Momentum: .
Step 2: Analysis
Initial momentum = (assuming total mass is ). Piece 1 momentum = . Piece 2 velocity = .
Step 3: Calculation
. Divide by : . .
Step 4: Conclusion
Hence, the velocity of the other piece is .
Final Answer:(C)

Step 1: Concept
Limiting friction .
Step 2: Analysis
Normal force N. .
Step 3: Calculation
Maximum friction force N. Applied force = 10 N. Since the applied force (10 N) is greater than the limiting friction (8 N), the block will move, and the frictional force acting is the kinetic friction (assumed equal to 8 N here).
Step 4: Conclusion
The force of friction is 8 newton.
Final Answer:(B)

Step 1: Concept
Conservation of Linear Momentum: Initial Momentum = Final Momentum.
Step 2: Analysis
Initial momentum = . Final state: The bullet is inside the block, so they move together as a single system of mass .
Step 3: Calculation
. .
Step 4: Conclusion
Hence, the final velocity is .
Final Answer:(A)

Step 1: Concept
Use Newton's Second Law ( ) and Kinematic Equations ( ).
Step 2: Analysis
Force ( ) = N (retarding force). Mass ( ) = 20 kg. Initial speed ( ) = 15 m/s. Final speed ( ) = 0 m/s (body stops).
Step 3: Calculation
Acceleration ( ) = m/ . Using : . s.
Step 4: Conclusion
Hence, the body takes 6 seconds to stop.
Final Answer:(A)

Static friction is the frictional force that resists the initiation of motion between two surfaces in contact. Unlike kinetic friction (which acts when there is motion), static friction varies depending on the external force applied.
Key property:
Static friction is self-adjusting. This means it increases as the applied force increases, but only up to a limit — the maximum static friction given by:
where is the coefficient of static friction and is the normal force.
Let’s analyze the options:
- (A) It always equals the maximum static friction: Incorrect — it only equals the maximum when motion is about to occur. Otherwise, it's less.
- (B) It is always less than kinetic friction: Incorrect — static friction is usually greater than kinetic friction.
- (C) It adjusts up to a maximum value to prevent motion: Correct — this is the defining feature of static friction.
- (D) It acts only when the body is moving: Incorrect — that's kinetic friction, not static.

When a block is placed on a rough horizontal surface and a horizontal force is applied, friction acts to oppose the applied force.
Since the block does not move, it is in equilibrium. This means the net force on it is zero.
Therefore, the frictional force must exactly balance the applied force:

This friction is called static friction. It is a self-adjusting force, meaning it increases or decreases to match the applied force—up to a maximum value called limiting friction.
The limiting friction is given by:
where is the coefficient of static friction and is the normal force.
If the applied force is less than the limiting friction, the static friction equals the applied force and the object remains at rest.
In this case, since the block does not move, we conclude:

So, the frictional force acting on the block is equal to the applied force.