IGNOU BPHCT-131 Solved Assignment 2023 | B.Sc (G) CBCS Abstract Classes ®

Solved By – Narendra Kr. Sharma – M.Sc (Mathematics Honors) – Delhi University

₹101.00

Get Instant Access

Share with your Friends

IGNOU BPHCT-131 Assignment Question Paper 2023

Course Code: BPHCT-131

Assignment Code: BPHCT-131//TMA/2023

Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.

\section*{PART A}

1. a) Determine two unit vectors perpendicular to both \(\vec{A}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{B}}=-2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}\).

b) For any two vectors \(\overrightarrow{\mathbf{u}}\) and \(\overrightarrow{\mathbf{v}}\) show that:

\[
(\overrightarrow{\mathbf{u}} . \overrightarrow{\mathbf{v}})^{2}-[(\overrightarrow{\mathbf{u}} \times \overrightarrow{\mathbf{v}}) \times \overrightarrow{\mathbf{v}}] . \overrightarrow{\mathbf{u}}=u^{2} v^{2}
\]

2. Solve the following ordinary differential equations:
a) \(\frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}+2 y=0, \quad y(0)=2, \quad y^{\prime}(0)=1\)
b) \(\frac{1}{x} \sin y d x+(\ln x \cos y+y) d y=0\)

3. a) A car has a weight of \(12,000 \mathrm{~N}\). The coefficient of kinetic friction between its wheels and the wet highway is 0.5 . The car is travelling at \(20 \mathrm{~ms}^{-1}\) when brakes are applied. How far does the car travel before it comes to a complete stop? Take \(g=10 \mathrm{~ms}^{-2}\).

b) A crate of mass \(20.0 \mathrm{~kg}\) is pulled by a force of \(180 \mathrm{~N}\), up an inclined plane which makes an angle of \(30^{\circ}\) with the horizon. The coefficient of kinetic friction between the plane and the crate is \(\mu_{\mathrm{k}}=0.225\). If the crates starts from rest, calculate its speed after it has been pulled \(15.0 \mathrm{~m}\). Draw the free body diagram.

c) A ball having a mass of \(0.5 \mathrm{~kg}\) is moving towards the east with a speed of velocity \(8.0 \mathrm{~ms}^{-1}\). After being hit by a bat it changes its direction and starts moving towards the north with a speed of \(6.0 \mathrm{~ms}^{-1}\). If the time of impact is \(0.1 \mathrm{~s}\), calculate the average force acting on the ball.

d) The vertical circular ride in an amusement park has a radius of \(40 \mathrm{~m}\). You are sitting in a car that is just at the top of the ride. How fast must the car be moving so that you momentarily lift off your seat and feel weightless? Take \(g=10 \mathrm{~ms}^{-2}\).

\section*{PART B}

4. a) A grinding wheel starts from rest and has a constant angular acceleration of \(5 \mathrm{rad} \mathrm{s}^{-2}\). At \(t=5 \mathrm{~s}\) find the total acceleration at a point \(1.0 \mathrm{~m}\) from the axis.

b) An insect of mass \(20 \mathrm{~g}\) crawls from the centre to the outside edge of a rotating disc of mass \(200 \mathrm{~g}\) and radius \(20 \mathrm{~cm}\). The disk was initially rotating at 22.0 rads \(^{-1}\). What will be its final angular velocity? c) The comet Encke has an aphelion distance of \(6.1 \times 10^{11} \mathrm{~m}\) and perihelion distance of \(5.1 \times 10^{11} \mathrm{~m}\). The mass of the sun is \(2.0 \times 10^{30} \mathrm{~kg}\). Calculate the speed of the comet at the perihelion.

d) The mass (in \(\mathrm{kg}\) ) and position coordinates (in \(\mathrm{m}\) ) of a system of three particles \(A\), \(B\) and \(C\) are as follows:

\(\begin{array}{ccc}\text { Particle } & \text { Mass } & \text { Position } \\ A & 2.0 \mathrm{~kg} & (0,0) \\ B & 1.0 \mathrm{~kg} & (2,0) \\ C & 3.0 \mathrm{~kg} & (1,1)\end{array}\)

Calculate the coordinates of the centre of mass of the system.

e) A particle of mass \(10.0 \mathrm{~kg}\), initially moving with a velocity of \(5.0 \mathrm{~ms}^{-1}\) collides elastically with a particle of mass \(5.0 \mathrm{~kg}\), initially moving with a velocity of \(-8.0 \mathrm{~ms}^{-1}\). What are the velocities of the two particles before and after the collision in the centre of mass frame of reference?

5. a) The amplitude of oscillation of a simple harmonic oscillator is \(40 \mathrm{~cm}\). Show that its instantaneous kinetic energy is less than its average kinetic energy when the displacement is \(30 \mathrm{~cm}\).

b) Two collinear harmonic oscillations are represented by:

\[
x_{1}=6 \sin \left(10 \pi t+\frac{\pi}{6}\right) \mathrm{cm} ; x_{2}=8 \sin \left(10 \pi t+\frac{\pi}{3}\right) \mathrm{cm}
\]

Calculate the amplitude, phase constant, and the period of resultant oscillation obtained on superposing these two collinear oscillations.

c) The quality factor of a sonometer wire is 3000 . The wire vibrates at a frequency of \(250 \mathrm{~Hz}\). Calculate the time in which its amplitude will reduce to half of its initial value.

d) A transverse wave travelling in the positive \(x\)-direction is given by \(y(x, t)=6 \sin (8 t-.05 x) \mathrm{cm}\), where \(x\) is in \(\mathrm{cm}\) and \(t\) is in seconds. Calculate the velocity of the wave and the maximum particle velocity.

BPHCT-131 Sample Solution 2023

Frequently Asked Questions (FAQs)

How do I access the Complete Solution?

You can access the Complete Solution through our app, which can be downloaded using this link:

App Link

Simply click “Install” to download and install the app, and then follow the instructions to purchase the required assignment solution. Currently, the app is only available for Android devices. We are working on making the app available for iOS in the future, but it is not currently available for iOS devices.

Is this Complete Solution for IGNOU Assignments?

Yes, It is Complete Solution, a comprehensive solution to the assignments for IGNOU. Valid from January 1, 2023 to December 31, 2023.

Is the Complete Solution aligned with the IGNOU requirements?

Yes, the Complete Solution is aligned with the IGNOU requirements and has been solved accordingly.

Is the Complete Solution guaranteed error-free?

Yes, the Complete Solution is guaranteed to be error-free.The solutions are thoroughly researched and verified by subject matter experts to ensure their accuracy.

Can I access the Complete Solution anytime?

As of now, you have access to the Complete Solution for a period of 6 months after the date of purchase, which is sufficient to complete the assignment. However, we can extend the access period upon request. You can access the solution anytime through our app.

What if I need help with a specific assignment question?

The app provides complete solutions for all assignment questions. If you still need help, you can contact the support team for assistance at Whatsapp +91-9958288900

Can I access the educational materials on multiple devices?

No, access to the educational materials is limited to one device only, where you have first logged in. Logging in on multiple devices is not allowed and may result in the revocation of access to the educational materials.

How do I make a payment for accessing the solutions?

Payments can be made through various secure online payment methods available in the app.Your payment information is protected with industry-standard security measures to ensure its confidentiality and safety. You will receive a receipt for your payment through email or within the app, depending on your preference.

What are the instructions for formatting my assignments?

The instructions for formatting your assignments are detailed in the Assignment Booklet, which includes details on paper size, margins, precision, and submission requirements. It is important to strictly follow these instructions to facilitate evaluation and avoid delays.

Terms and Conditions

The educational materials provided in the app are the sole property of the app owner and are protected by copyright laws.
Reproduction, distribution, or sale of the educational materials without prior written consent from the app owner is strictly prohibited and may result in legal consequences.
Any attempt to modify, alter, or use the educational materials for commercial purposes is strictly prohibited.
The app owner reserves the right to revoke access to the educational materials at any time without notice for any violation of these terms and conditions.
The app owner is not responsible for any damages or losses resulting from the use of the educational materials.
The app owner reserves the right to modify these terms and conditions at any time without notice.
By accessing and using the app, you agree to abide by these terms and conditions.
Access to the educational materials is limited to one device only. Logging in to the app on multiple devices is not allowed and may result in the revocation of access to the educational materials.

Our educational materials are solely available on our website and application only. Users and students can report the dealing or selling of the copied version of our educational materials by any third party at our email address (abstract4math@gmail.com) or mobile no. (+91-9958288900).

In return, such users/students can expect free our educational materials/assignments and other benefits as a bonafide gesture which will be completely dependent upon our discretion.