Mechanics - C - BU 2021 Question Paper

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B.A. III^rd Year (Reg./Pvt.) Main Examination, 2021

Mathematics

Paper - III

Mechanics - C

[Maximum Marks : Reg. 40
Pvt. 50

नोट :- प्रत्येक खंड से पूछे गये प्रश्नों के अंक समान हैं । प्रत्येक खंड का उत्तर नवीन पृष्ठ से प्रारंभ करें । उत्तरपुस्तिका की संख्या लगभग 16 पृष्ठ होगी । विद्यार्थी द्वारा स्वयं की हस्तलिपि में उत्तर लिखें अनिवार्य है । उत्तरपुस्तिका का प्रथम पृष्ठ विश्वविद्यालय की वेबसाइट से डाउनलोड करना अनिवार्य है । ( प्रत्येक प्रश्न का उत्तर लगभग 250 शब्दों से अधिक न हो । )

Note:- All questions from each section carry equal marks. All questions are compulsory and answer limit are approximately 250 words. Start the answer of each section from new page. Maximum limit of pages of answer booklet are approximately 16 pages. Answer should be written by the student in his/her own handwriting mandatory. The first page of answersheet should be download by the student from university website is mandatory.

रेखाओं x=0, y=0 और 3x + 4y = 5 द्वारा निर्मित एक त्रिभुज, जो अ बलों P, 2P, 3P क्रियाशील हैं । परिणामी का परिमाण और उसकी क्रिया रेखा का समीकरण ज्ञात कीजिए ।

Forces P, 2P, 3P act along the sides of a triangle formed by the lines x = 0, y = 0 and 3x + 4y = 5. Find the magnitude of the resultant and the equation of its line of action.

कैटेनरी का कार्तीय समीकरण ज्ञात कीजिए।

Find the cartesian equation of catenary.

दर्शाइए कि दो बल निकाय ये संयोगी रेखाओं का केवल एक ही जोड़ा, जो उभयनिष्ठ रखते हैं ।

Show that in general two system of forces have only one pair of conjugate lines in common.

बल निकाय (X, Y, Z, L, M, N) के लिए तल x + y + z = 0 का निष्प्रभावी बिन्दु ज्ञात कीजिए।

Find the null point of the plane x + y + z = 0 for the system force (X, Y, Z, L, M, N).

एक कण परवलय p² = ar पर गतिमान है जिसका नाभि के परितः कोणीय वेग अचर है । सिद्ध कीजिए कि इसकी भिलंब दूरी इसकी वक्रता त्रिज्या के समानुपाती होती है ।

A particle is moving in a parabola p² = ar with uniform angular velocity about the focus. Prove that its normal acceleration, at any point is proportional to the radius of curvature of its path at that point.