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BPHCT 131: Mechanics

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Title Name IGNOU BSCFBC BPHCT 131 Mechanics Solved Assignment ENGLISH
Type Soft Copy (E-Assignment) .pdf
University IGNOU
Degree BACHELOR DEGREE PROGRAMMES
Course Code BSCFBC
Course Name Bachelor of Science (Biochemistry)
Subject Code BPHCT 131
Subject Name Mechanics
Year 2026
Session -
Language ENGLISH
Assignment Code BPHCT 131/Assignment-1/2026
Product Description Assignment of BSCFBC (Bachelor of Science (Biochemistry)) 2026. Latest BPHCT 131 2026 Solved Assignment Solutions
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BPHCT 131 (January 2026 - July 2026) - ENGLISH

Tutor Marked Assignment
MECHANICS

Course Code: BPHCT-131
Assignment Code: BPHCT-131//TMA/2026
Max. Marks: 100

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

PART A
1. a) Three vectors equation, equation and equation satisfy the condition equation. If equation and equation determine the value of equation. (5)

b) A curve is described by the following parametric equations
equation
Determine the unit tangent vector to the curve at the point equation. 

2. Solve the following ordinary differential equations:
a) equation 
b) equation 

3. a) The maximum speed with which a equation car can make a turn in a circular path is equation. The radius of the circle in which the car is turning is equation. Determine the force of friction being exerted upon the car and the coefficient of friction between the car and the road. Take equation. 

b) An equation person jumping from a height of equation hits the ground with a speed of nearly equation. Calculate the impulse experienced by the person during the collision with ground and the average force exerted on the person, if the collision with the ground lasts for equation. 

c) A girl of mass equation stands in an elevator. Obtain the force which the floor of the lift exerts on the girl
i) when the lift has an upward acceleration of equation; ii) when the lift is rising at constant speed and iii) when the lift has a downward acceleration of equation. Draw the free body diagram. Take equation. 

d) A block of mass equation is moved up from the base a rough inclined plane making an angle of equation with the horizontal with initial speed equation. The coefficient of kinetic friction between the block and the plane is 0.2. Calculate
i) the maximum distance the block travels up the incline before coming to rest.
ii) the speed of the block when it returns to the base of the inclined plane.
iii) the energy lost over the entire motion. Take equation. 

PART B

4. a) A uniform disk of mass equation and radius equation is initially at rest on a frictionless vertical axle. A constant tangential force of equation is applied at the edge of the disk for equation. Determine the i) the angular acceleration of the disk ii) the angular speed after equation iii) the angular momentum of the disk after equation, and iv) the rotational kinetic energy after equation. 

b) A particle A of mass equation moving along the x-axis with speed equation collides elastically with a particle B of equal mass which is initially at rest. After the collision, particle A moves at an angle of equation above the x-axis. Calculate the velocities of the two particles after the collision. 

c) Given that the time period of Halley's comet is equation, calculate the length of its semi-major axis. If the perihelion distance of the orbit is equation, calculate the aphelion distance. 

5. a) An object undergoes SHM with frequency equation. The initial displacement is equation and the initial velocity is equation. Calculate the amplitude, maximum velocity and maximum acceleration of the object.

b) Two collinear harmonic oscillations, each of frequency equation, have amplitudes, a1 and a2 and initial phases, equation and equation, respectively. Show that, when these oscillations are superposed, the amplitude of the resultant motion is equal to (a1 - a2). What will be the value of the resultant amplitude when equation and equation. 

c) Restoring and frictional forces of magnitudes kx and equation, respectively act simultaneously on an object of mass equation attached to a spring. Under the influence of these forces, the mass oscillates with a frequency equation and its amplitude reduces to half in equation. Calculate the damping constant equation, the force constant k and the damping factor b. Also write the differential equation for the system. 

d) A progressive wave is described by
equation$
Determine its direction of propagation and calculate the amplitude, wave number, wavelength and frequency of the wave. 
 


BPHCT 131 (January 2026 - July 2026) - HINDI

अध्यापक जांच सत्रीय कार्य
यांत्रिकी

पाठ्यक्रम कोड : BPHCT-131
सत्रीय कार्य कोड : BPHCT-131/TMA/2026
अधिकतम अंक : 100

नोट : सभी प्रश्न हल करें। प्रत्येक प्रश्न के अंक उसके सामने दिए गए हैं।

भाग क

1. क) तीन सदिश equation, equation और equation प्रतिबंध equation को संतुष्ट करते हैं। यदि equation और equation तो equation का मान ज्ञात करें। (5)

ख) एक वक्र को निम्नलिखित प्राचलिक समीकरणों (parametric equations) द्वारा निरूपित किया जाता है :
equation
बिन्दु equation पर इस वक्र पर एकक स्पर्शी सदिश ज्ञात करें। 

2. निम्नलिखित साधारण अवकल समीकरणों का हल प्राप्त करें :
क) equation ; equation के लिए। 
ख) equation

3. क) द्रव्यमान equation की एक कार वर्तुल पथ पर equation की अधिकतम चाल से मुड़ सकती है। कार जिस वृत्त में मुड़ती है, उसकी त्रिज्या equation है। कार पर लग रहा घर्षण बल और कार और सड़क के बीच घर्षण गुणांक प्राप्त करें। equation लें।

ख) द्रव्यमान equation का एक व्यक्ति, equation की ऊंचाई से कूदता है और लगभग equation की चाल से जमीन पर गिरता है। यदि व्यक्ति के जमीन से टकराने का समयांतराल 0.1 सेकंड हो, तो जमीन से संपर्क के दौरान व्यक्ति द्वारा अनुभव किया गया आवेग और उस पर लगने वाले औसत बल की गणना करें । 

ग) द्रव्यमान equation वाली एक बच्ची लिफ्ट में खड़ी है। बच्ची पर लिफ़्ट के फर्श द्वारा लगाया गया बल प्राप्त करें जब i) लिफ़्ट का ऊपर की ओर त्वरण equation हो ii) लिफ़्ट ऊपर की और अचर चाल से चल रही हो, और iii) लिफ़्ट का नीचे की ओर त्वरण equation हो। बल-निर्देशांक आरेख भी खींचें। equation लें।

घ) द्रव्यमान equation के एक खंड को एक खुरदरे नत तल पर, आधार से equation की प्रारंभिक चाल से ऊपर की ओर गतिमान किया जाता है। नत ताल क्षैतिज के साथ equation का कोण बनाती है। खंड और नत तल के बीच गतिक घर्षण गुणांक 0.2 है। गणना करें :
i) विराम अवस्था में आने से पहले खंड द्वारा नत तल पर तय की गई अधिकतम दूरी।
ii) नत तल के आधार पर वापस आने पर खंड की चाल।
iii) इस सम्पूर्ण गति में क्षयित ऊर्जा। equation लें। 

भाग ख

4. क) एक घर्षणहीन ऊर्ध्वाधर धुरी पर स्थित द्रव्यमान equation और त्रिज्या equation वाली एक डिस्क प्रारम्भ में विरामस्थ है। डिस्क के किनारे पर equation के लिए equation का एक अचर स्पर्शरेखीय बल लगाया जाता है। डिस्क का i) कोणीय त्वरण ii) equation के बाद कोणीय चाल iii) equation के बाद कोणीय संवेग, और iv) equation के बाद घूर्णी गतिज ऊर्जा ज्ञात करें।

ख) equation द्रव्यमान का एक कण A, x-अक्ष के अनुदिश equation के चाल से गतिमान है और समान द्रव्यमान के एक विरामस्थ कण B से प्रत्यास्थ संघट्टन करता है। संघट्टन के बाद, कण A x-अक्ष से ऊपर equation के कोण पर गति करता है। संघट्टन के बाद दोनों कणों की चालों की गणना करें। 

ग) यदि हैली पुच्छल तारे का आवर्तकाल 75.3 वर्ष हो, तो उसके अर्ध-दीर्घ अक्ष की लंबाई ज्ञात करें। यदि कक्षा के रविनीच दूरी का मान equation है, तो रविउच्च दूरी के मान की गणना करें। 

5. क) एक पिंड सरल आवर्त गति करता है जिसकी आवृत्ति, equation, प्रारंभिक विस्थापन equation तथा प्रारंभिक वेग equation है। पिंड के दोलन का आयाम, अधिकतम वेग तथा अधिकतम त्वरण परिकलित करें। 

ख) दो संरेख आवर्ती दोलनों की आवृत्ति equation है तथा उनके आयाम a1 एवं a2 और प्रारंभिक कलाएं क्रमशः equation एवं equation हैं। सिद्ध करें कि यदि इन दोलनों को अध्यारोपित किया जाए तो परिणामी गति का आयाम (a1 - a2) होगा। यदि equation एवं equation हो तो परिणामी आयाम का मान क्या होगा? 

ग) एक कमानी से लटके equation द्रव्यमान वाले पिंड पर क्रमशः kx एवं equation परिमाण के प्रत्यानयन एवं घर्षण बल एक साथ कार्यरत हैं। इन बलों के प्रभाव में द्रव्यमान equation आवृत्ति के दोलन करता है और दोलन आयाम equation में आधा हो जाता है। बल नियतांक k, अवमंदन नियतांक equation तथा अवमंदन गुणक b के मान परिकलित करें तथा निकाय का अवकल समीकरण लिखें। (4+2+2+2)

घ) एक प्रगामी तरंग को नीचे दिए गए समीकरण द्वारा निरूपित किया जाता है :
equation$
इस तरंग की संचरण दिशा निर्धारित करें तथा इसका आयाम, तरंग संख्या, तरंगदैर्घ्य एवं आवृत्ति परिकलित करें।

 


BPHCT 131 2025 - English

Tutor Marked Assignment

MECHANICS

Course Code: BPHCT-131

Assignment Code: BPHCT-131//TMA/2025 Max.

Marks: 100

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

PART A

1. a) Determine the torque about the point (0, 1, 1) due to a force equation being exerted at the point (4, 2, 3).

b) Given two vector functions equation and equation ,determine the derivative of equation at t=1.

2. Solve the following ordinary differential equations:

a) equation

b) equation for y(o) = 2, equation.

3. a) A box of mass 10 kg is being pulled on the floor by a mass-less rope with a force of 100 N at an angle of 600 to the horizontal. What is the acceleration of the box if the coefficient of kinetic friction between the floor and the box is uk = 0.25? Take g = 10 ms-2 

b) A ball having a mass of 0.5 kg is moving towards the east with a speed of velocity 6.0 ms-1. After being hit by a bat it changes its direction and starts moving towards the north with a speed of 5.0 ms-1. If the time of impact is 0.1 s, calculate the impulse and average force acting on the ball.

c) A block of mass 5.0 kg starts from rest and slides down a surface which corresponds to a quarter of a circle of 3.0 m radius. (i) If the curved surface is smooth, find the speed at the bottom. (ii) If the speed at the bottom is 2.0 ms-1, calculate the energy dissipated due to friction in the descent. (iii) After the block reaches the horizontal with a speed of 2.0 ms-1it slides to a stop in a distance of 1.5 m. calculate the frictional force acting on the horizontal surface. Take g= 10 ms -2  

d) A small satellite is in a circular orbit around a planet at a distance of 4.0 x 10 8 m from the centre of the planet. The orbital speed of the satellite is 200 ms-1 What is the mass of the planet?

PART B

4. a) A solid cylinder of mass 3.0 kg and radius 1.0 m is rotating about its axis with a speed of 40 rad s-1. Calculate the torque which must be applied to bring it to rest in 10s. What would be the power required?

b) A proton undergoes a head on elastic collision with a particle of unknown mass Initially at rest and rebounds with 16/25 of its initial kinetic energy. Calculate the ratio of the mass of the unknown particle with respect to the mass of the proton.

c) The planet Jupiter has an elliptical orbit e =.05 and a semi major axis of 7.8 x 1011 m  . Find the energy of the planet and the perihelion and aphelion distances.

5. a) A simple harmonic oscillator has amplitude 15 cm and it completes 100 oscillations in 50 s. (i) Calculate its time period and angular frequency. (ii) If the initial phase is π/2, write expressions for its displacement and velocity. (iii) Calculate the values of maximum velocity and acceleration.

b) For a damped harmonic oscillation, the equation of motion is

equation

with m = 0.25kg, y= 0.05kgs-1 and 70Nm -1 Calculate (i) the period of motion, (ii) number of oscillations in which its amplitude will become half of its initial value, and (iii) the number of oscillations in which its mechanical energy will drop to half of its initial value.

c) The equation of transverse wave on a rope is

y(x, t) = 10 sin (6.0t − 0.05x)

where y and x are measured in cm and t is expressed in second. Calculate the maximum speed of a particle on the rope.


BPHCT 131 2025 - Hindi

अध्यापक जांच सत्रीय कार्य

यांत्रिकी

पाठ्यक्रम कोड: BPHCT-131

सत्रीय कार्य कोड: BPHCT-131/TMA/2025

अधिकतम अंक : 100

नोट: सभी प्रश्न हल करें। प्रत्येक प्रश्न के अंक उसके सामने दिए गए हैं।

भाग क

1. क) बिन्दु (4, 2, 3) पर लग रहे बल equation के कारण बिन्दु (0, 1, 1) के प्रति बल आघूर्ण की गणना करें। (5)

ख) दो सदिश फलनों  equation  औरequation  के लिए t = 1 पर  equation का अवकलज ज्ञात करें। 

2. निम्नलिखित साधारण अवकल समीकरणों का हल प्राप्त करें :

क) equation

ख) equation के लिए। 

3. क) द्रव्यमान 10 kg वाले एक बक्से को फर्श पर द्रव्यमानहीन रस्सी द्वारा क्षैतिज से 60° के कोण पर 100 N के बल से खींचा जाता है। यदि फर्श और बक्से के बीच गतिक घर्षण गुणांक µε = 0.25 हो तो बक्से के त्वरण की गणना करें। g = 10ms-2 लें । 

ख) द्रव्यमान 0.5 kg वाली एक गेंद 6.0 ms -1 की चाल से पूर्व दिशा की ओर गतिमान है। बल्ले से मारे जाने पर वह अपनी दिशा बदलती है और 5.0 ms -1 की चाल से उत्तर दिशा में गतिमान हो जाती है। यदि टक्कर की अवधि 0.1s हो, तो आवेग और गेंद पर लगने वाला औसत बल परिकलित करें।

ग) द्रव्यमान 5.0 kg का एक खण्ड विरामावस्था से प्रारंभ करके एक सतह पर नीचे फिसलता है। उस सतह का आकार 3.0m त्रिज्या वाले वृत्त के चतुर्थांश जैसा है। (i) यदि वक्राकार सतह चिकनी हो तो सतह के निम्नतम बिंदु पर खण्ड के चाल की गणना करें। (ii) यदि सतह के निम्नतम बिंदु पर खण्ड की चाल 2.0 ms -1 हो तो जब वह नीचे फिसलता है तो घर्षण के कारण कितनी ऊर्जा का क्षय होता है? (iii) जब खण्ड क्षैतिज सतह पर 2.0 ms -1 की चाल से पहुंचता है, तो वह निम्नतम बिंदु से 1.5m की दूरी तय करने के बाद रुक जाता है। खण्ड के कारण क्षैतिज सतह पर लग रहा घर्षण बल ज्ञात करें। g = 10ms -2 लें । 

घ) एक ग्रह के केंद्र से दूरी 4.0 × 108 m पर एक छोटा उपग्रह ग्रह के चारों ओर वृत्ताकार कक्षा में परिक्रमा कर रहा है। उपग्रह की कक्षीय चाल 200 ms -1 है। ग्रह का द्रव्यमान क्या है? 

भाग ख

4. क) द्रव्यमान 3.0 kg और 1.0 m त्रिज्या वाला एक ठोस बेलन अपने अक्ष के प्रति 40 rad s-1की चाल से घूर्णन कर रहा है। 10s में उसे विरामस्थ करने के लिए कितने बल आघूर्ण की आवश्यकता होगी? इसमें कितनी शक्ति का प्रयोग होगा?

ख) एक प्रोटॉन का अज्ञात द्रव्यमान वाले एक कण के साथ सीधा प्रत्यास्थ संघट्टन होता है, जो आरंभ में विरामावस्था में है। संघट्टन के बाद लौटने पर प्रोटॉन की गतिज ऊर्जा उसकी आरंभिक गतिज ऊर्जा का 16/25 भाग है। अज्ञात द्रव्यमान और प्रोटॉन के द्रव्यमान का अनुपात ज्ञात करें।

ग) बृहस्पति की दीर्घवृत्तीय कक्षा के लिए 0.05 है और अर्ध-दीर्घ अक्ष 7.8×10¹¹m है। ग्रह की ऊर्जा तथा रविनीच और रविउच्च बिंदुओं की दूरियां ज्ञात करें।

(i) इस दोलक का आवर्तकाल और कोणीय आवृत्ति परिकलित करें। (ii) यदि इस दोलक की

5. क) एक सरल आवर्त दोलक का आयाम 15 cm है और यह 50s में 100 दोलन पूरे करता है। प्रारंभिक कला equation/2 है तो इसके विस्थापन और वेग के लिए व्यंजक लिखें। (iii) इसके वेग तथा त्वरण का अधिकतम मान परिकलित करें।

ख) किसी अवमंदित आवर्त दोलक का गति समीकरण निम्नलिखित है :

equation

जहां m = 0.25kg, y = 0.05kgs-1 तथा k = 70Nm 1 है। (i) दोलन काल, (ii) दोलनों की संख्या जिसके बाद आयाम का मान उसके आरंभिक मान का आधा रह जाता है, (iii) दोलनों की संख्या जिसके बाद दोलक की यांत्रिक ऊर्जा का मान उसके आरंभिक मान का आधा रह जाता है, परिकलित करें।

ग) किसी तार पर अनुप्रस्थ तरंग का व्यंजक है :

y(x, t) = 10 sin (6.0t - 0.05x)

जहां y तथा x cm में तथा सेकंड में हैं। तार के किसी कण की अधिकतम चाल परिकलित करें।

 

 

 

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