Laws Of Motion

The correct option is (B): 5 m/s²

f_max = µN = µMg = (0.5) (10) (10) = 50 N
a =
= 100 –
= 5 m/sec²

The maximum mass value of block B to prevent the two blocks from moving is determined by the maximum static friction force (F_max). This force can be calculated using the coefficient of static friction (µs) and the weight of block A (W_A).

Given:

• Mass of block A (m_A) = 2 kg
• Coefficient of static friction (µs) = 0.2

First, calculate the weight of block A (W_A): W_A = m_A g W_A = 2 kg 9.81 m/s² ≈ 19.62 N

Now, determine the maximum static friction force (F_max): F_max = µs N F_max = 0.2 19.62 N ≈ 3.924 N

So, the maximum mass value of block B should not exceed the force of approximately 3.924 N to prevent the two blocks from moving.

Let v be the tangential speed of the heavier stone. Then, the centripetal force experienced by lighter stone is
and that of heavier stone is

But it is given that (F_c)_{lighter =} (F_c)_heavier

n² = 4

n = 2

Calculation of Velocity and Momentum

Given that the velocity of the block is derived from the energy equation:

Next, applying the principle of conservation of momentum, we have:

Now, let's apply the given values to the momentum equation:

Simplifying and solving for :

Speed Calculation

We are given an equation involving velocity, the coefficient of static friction, and the angle . Let's break down the steps to find the velocity .

Step 1: Given Equation

The given equation is:

Where: - is the velocity, - is the radius of the curve, - is the acceleration due to gravity, - is the coefficient of static friction, - is the angle of the curve.

Step 2: Solving for

To solve for , multiply both sides of the equation by and take the square root:

Now, take the square root of both sides to get :

Conclusion:

The velocity is given by:

Height = 180 m
Therefore, the correct option is (A) : after 2s at a height 180 m

To find the value of the unknown mass such that the rod is in equilibrium, we need to apply the principles of moments (torques). A system is in equilibrium when the sum of the clockwise moments about any pivot is equal to the sum of the counterclockwise moments.

Let's analyze the problem step by step:

1. The rod is 200 cm long and has a mass of 500 g (0.5 kg). The center of mass of the rod is at its midpoint, i.e., at 100 cm from either end. However, since it's pivoted at the 40 cm mark, the distance of the center of mass from the pivot is (100 cm - 40 cm).
2. The downward force due to the weight of the rod is .
3. Given:
   • A 2 kg mass is hung at the 20 cm mark, creating a downward force of . The distance from the pivot is .
   • An unknown mass is hung at the 160 cm mark. The downward force is . The distance from the pivot is .
4. The moment due to the 2 kg mass is (counterclockwise).
5. The moment due to the weight of the rod is (clockwise).
6. The moment due to mass is (clockwise).

For equilibrium, the sum of clockwise moments should equal the sum of counterclockwise moments:

Simplifying:

Thus, the value of the unknown mass is kg.

To solve the given problem, let's break it down step by step and use the necessary physics concepts and formulae:

Understanding the Problem: A particle is moving in a circular path with radius and uniform speed, completing one full revolution in time . When projected at an angle with the initial speed, the particle's maximum height ( ) is given as .

Formulas and Concepts:

• The speed of the particle in the circular path can be calculated using the formula for the circumference of the circle: .
• For projectile motion, the vertical component of velocity is , and the horizontal component is .
• The maximum height for a projectile is given by: .

Substitute Values:

• From the given information, . Therefore, we equate it to the expression for height: .
• Substitute into the equation: .

Solve for :

• Solve the equation for : .
• Simplify to find: .
• Thus, the angle of projection can be expressed as: .

Conclusion: The correct option is: . This matches the given correct answer.

To solve the problem, we will calculate the magnitude of the impulse imparted to the ball when it hits the ground and rebounds. The relevant concepts include impulse and momentum. Impulse is defined as the change in momentum of the object.

1. The initial velocity ( ) of the ball just before it strikes the ground can be calculated using the equation for velocity under gravity: , where and .

1. When the ball rebounds to the same height, its final velocity ( ) at the point of impact upon rebounding will be equal in magnitude but opposite in direction to . Thus, .
2. Impulse ( ) is given by the change in momentum, which can be expressed as: , where .

1. We take the magnitude of impulse as which, when rounded, is approximately .

Therefore, the magnitude of the impulse imparted to the ball is approximately 4.2 kg m/s, which corresponds with option 3.

To find the minimum power delivered by the motor to the lift, we need to consider both the force needed to overcome gravity and the frictional force. The power required by the motor can be calculated using the formula:

where is the total force opposing the lift's movement, and is the velocity of the lift.

First, calculate the gravitational force :

Given: (mass of the lift + passengers), (acceleration due to gravity).
Therefore,

Next, add the gravitational force and the frictional force to get the total force:

Now, use the formula for power:

Thus, the minimum power delivered by the motor is 34500 watts.