Newtons Laws Of Motion

Step 1: Convert mass into SI units.


Step 2: Calculate impulse.
Impulse
Magnitude of impulse .

Step 3: Calculate average force.


Step 4: Conclusion.
Impulse and average force .

Step 1: Understanding the scenario.
The two masses and are connected and subjected to uniform acceleration on a frictionless surface. The tension in the string connecting them is and , respectively. We need to find the ratio .
Step 2: Applying Newton’s second law.
For mass , the tension causes an acceleration , so: For mass , the tension causes an acceleration , so: Step 3: Finding the ratio of tensions.
From equations (1) and (2), we can write: But since both masses are moving together, the total mass being accelerated is . So, the ratio of the tensions becomes: Step 4: Conclusion.
Therefore, the correct ratio of the tensions is , which corresponds to option (C).

Step 1: Photoelectric equation.
Stopping potential is given by
Step 2: Effect of threshold frequency.
For a fixed incident frequency , a lower threshold frequency gives a larger value of , and hence a larger stopping potential.
Step 3: Interpreting the graph.
From the graph, metal A has the lowest threshold frequency among A, B, C and D.
Step 4: Conclusion.
Therefore, metal A has the highest stopping potential for the given frequency.

Step 1: Understand rocket propulsion.
A rocket moves upward by ejecting gases downward at high speed.
Step 2: Apply conservation law.
In absence of external forces, total linear momentum of rocket and exhaust gases remains conserved.
Step 3: Explain motion.
Downward momentum of gases produces equal upward momentum of the rocket.
Step 4: Conclusion.
Rocket propulsion is based on conservation of linear momentum.

Step 1: Understanding the coefficient of restitution.
The coefficient of restitution ( ) is the ratio of the speed of separation to the speed of approach. When the ball hits the ground, the velocity of the ball just before the impact is given by , where is the height and is the acceleration due to gravity. After the collision, the velocity is reduced by the coefficient of restitution. Therefore, the rebound height will be related to the square of .
Step 2: Calculating the rebound height.
The velocity just before the rebound is: The rebound velocity is reduced by the factor , so the rebound velocity is: Now, the maximum height after the rebound is given by: Step 3: Conclusion.
Thus, the maximum height of the ball after the first rebound is 0.8 m, corresponding to option (A).

Step 1: Calculate normal reaction.


Step 2: Calculate maximum static friction.


Step 3: Compare applied force with limiting friction.
Applied force
So the block does not move.

Step 4: Frictional force.
For static condition, friction equals the applied force.


Step 5: Conclusion.
The force of friction acting on the block is .

Step 1: Using the relation for stopping distance.
The stopping distance is proportional to the square of the speed. Hence, if the stopping distance for a speed is , then for a speed , the stopping distance is given by: Substituting the given values: Step 2: Conclusion.
The correct answer is (B), 45 m.

Step 1: Flow rate from holes.
The flow rate through an orifice is given by Torricelli's law: where is the discharge coefficient, is the area of the hole, is the acceleration due to gravity, and is the height of the fluid above the hole.
Step 2: Apply to both holes.
For the square hole, the area is , and the depth is . For the circular hole, the area is , and the depth is . The flow rates should be equal, so: Simplifying: Thus:
Step 3: Conclusion.
The correct relation between and is , so the correct answer is (D).

Step 1: Use Newton’s second law.
A constant force acting on a mass produces acceleration
Step 2: Find velocity after time .
Since the body starts from rest,
Step 3: Write expression for kinetic energy.

Step 4: Substitute the value of velocity.

Step 5: Conclusion.
The kinetic energy of the body at time is .

Step 1: Understanding the forces.
The net force exerted by the surface is the resultant of the frictional force and the force due to gravity. The frictional force , where is the normal force.
Step 2: Finding the net force.
The net force can be expressed as the square root of the sum of the squared forces, i.e., Step 3: Conclusion.
The correct answer is (D), .

Step 1: Finding velocity.
Velocity is the derivative of displacement with respect to time. The displacement is given by: Taking the derivative with respect to time : Step 2: Finding acceleration.
Acceleration is the derivative of velocity with respect to time. Taking the derivative of : Step 3: Finding force.
Force is given by . Substituting the values for mass and acceleration at : Thus, the force is: Thus, the correct answer is (A) 150 N.

Step 1: Formula for momentum
Momentum is given by the product of mass and velocity:
Step 2: Substitute the given values
Given: - Mass - Velocity
Answer:
Therefore, the momentum of the object is . So, the correct answer is option (1).

Step 1: Use the formula for average speed Given: - Total distance = 200 m - Total time = 20 s Substitute the values into the formula: Answer: Therefore, the average speed of the car is . So, the correct answer is option (1).

According to Newton’s Second Law: Given: Force , Mass Rearranging to solve for acceleration: Option (b) is correct.

Step 1: Use the kinematic equation to find the maximum height At the maximum height, the final velocity . The equation for vertical motion is: Where: - is the final velocity - is the initial velocity - is the acceleration due to gravity - is the maximum height Given: - - - Rearrange the formula to solve for height : Answer: Therefore, the maximum height reached by the ball is . So, the correct answer is option (1).

Step 1: Use Newton's second law of motion Where: - is the applied force - is the mass of the block - is the acceleration Given: - - Rearranging the formula to solve for acceleration : Answer: Therefore, the acceleration of the block is . So, the correct answer is option (1).

Concept: According to Newton's Second Law of Motion, where

• = net force acting on the body
• = mass of the body
• = acceleration produced

Thus,
Step 1: {Write the given values.}
Step 2: {Substitute into the formula.}
Step 3: {State the final result.} Hence, the acceleration of the block is