क) तीन सदिश ,
और
प्रतिबंध
को संतुष्ट करते हैं। यदि
और
तो
का मान ज्ञात करें।
हमारे पास तीन सदिश (\vec{a}, \vec{b}, \vec{c}) हैं, जो निम्नलिखित शर्त को संतुष्ट करते हैं: [ \vec{a} + \vec{b} + \vec{c} = \vec{0}. ] हमें दिया गया है: [ |\vec{a}| = 4, \quad |\vec{b}| = 2, \quad |\vec{c}| = 3 ] ____ __________ _____ _______ ______ __________ ____ _______ ___ _____ ______ ___.
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_______ ________ ____ ________ _________ ___ _______ _________.
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The maximum speed with which a car can make a turn in a circular path is
. The radius of the circle in which the car is turning is
. Determine the force of friction being exerted upon the car and the coefficient of friction between the car and the road. Take
.
एक वक्र को निम्नलिखित प्राचलिक समीकरणों (parametric equations) द्वारा निरूपित किया जाता है :
बिन्दु पर इस वक्र पर एकक स्पर्शी सदिश ज्ञात करें।
A progressive wave is described by$
Determine its direction of propagation and calculate the amplitude, wave number, wavelength and frequency of the wave.
एक पिंड सरल आवर्त गति करता है जिसकी आवृत्ति, , प्रारंभिक विस्थापन
तथा प्रारंभिक वेग
है। पिंड के दोलन का आयाम, अधिकतम वेग तथा अधिकतम त्वरण परिकलित करें।
A uniform disk of mass and radius
is initially at rest on a frictionless vertical axle. A constant tangential force of
is applied at the edge of the disk for
. Determine the i) the angular acceleration of the disk ii) the angular speed after
iii) the angular momentum of the disk after
, and iv) the rotational kinetic energy after
.
An person jumping from a height of
hits the ground with a speed of nearly
. 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
.
Two collinear harmonic oscillations, each of frequency , have amplitudes, a1 and a2 and initial phases,
and
, 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
and
.