Work Energy And Power

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An object's mass times its velocity is said to have linear momentum. A vector quantity, that is. The letter "p" stands for it. A body's momentum and velocity both point in the same general direction. The overall momentum of an isolated system remains constant since momentum is a conserved quantity. Kg m/s is the SI unit for linear momentum.

Given by is the formula for a body's linear momentum.

p = m⋅v

Where,

m = the object's mass

v = the object's velocity

Now, linear momentum is calculated using the formula,

linear momentum = mass × velocity

So, the dimensional formula of linear momentum can be calculated using the above formula

Dimensional formula of mass = [M¹L⁰T⁰]

Dimensional formula of velocity = [M⁰L¹T^-1]

Dimensional Formula of linear momentum = [M¹L⁰T⁰] × [M⁰L¹T^-1] = [M¹L¹T^-1]

Therefore, the dimensional formula of linear momentum is [M¹L¹T^-1].

The correct option is (A) : 100%

P1 = mE₁ ; P2 = mE₂

= m( ) =√2m(4E₁)=2P₁

∴ % change = = =100%

m₁v₁ = m₂v₂ (P₁ = P₂);

= =

The correct answer is Option B) by the system against a conservative force

Potential energy will increase when work is done by the system against a conservative force.

-U = W_{conservative force}

Discover More From Chapter: Work, Energy and Power

Calculation of Tangential Acceleration

The correct option is (D): 0.1 m/s².

Step-by-Step Calculation:

We are given the following equation for kinetic energy:

Substituting values:

Simplifying further:

The initial velocity of the particle is:

Finding Tangential Acceleration

We are asked to find the tangential acceleration at the end of the 2nd revolution. First, we calculate the total distance covered:

Now, using the equation for motion:

Solving for acceleration :

Substituting known values:

Finally, simplifying:

Conclusion:

The tangential acceleration at the end of the 2nd revolution is approximately , so the correct option is (D).

Force, Velocity, and Power Calculation

We are given the force as a function of time and need to calculate the velocity and power of the object:

Step 1: Given Force

The force acting on the object is given by:

Step 2: Using Newton's Second Law of Motion

According to Newton's second law, the force is related to the rate of change of velocity:

Where: - (mass of the object), - is the velocity of the object, - is time.

Step 3: Finding the Velocity

We now integrate the equation with respect to time to find the velocity. The equation becomes:

Performing the integration, we get:

This gives the velocity of the object as a function of time:

Step 4: Calculating the Power

The power delivered by the force is the dot product of the force and velocity vectors:

Substitute the expressions for and :

Now compute the dot product:

Conclusion:

The power delivered by the force as a function of time is:

Work Calculation Explanation

We are asked to calculate the work done by a force over a displacement . The formula for work is:

Step 1: Given Values

The force and displacement are given as:

Step 2: Simplify Displacement

Now, let's simplify the displacement vector :

First, distribute the negative sign:

Now, simplify the terms:

Step 3: Dot Product Calculation

Next, we calculate the dot product of the force and displacement vectors:

Step 4: Perform the Dot Product

To compute the dot product, we multiply corresponding components and sum them:

• For the -component:
• For the -component:
• For the -component: (since there's no -component in )

So, the dot product is:

Conclusion:

The work done is 5 Joules (J).