By R.K. Shukla
Compatible for numerous aggressive examinations and for the 1st 12 months engineering scholars, this publication includes diagrams, worked-out examples and similar questions-answers.
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Additional info for Mechanics
This is called ‘instantaneous acceleration’ and is given by → a = Lim ∆t → 0 ∆v dv = ∆t dt The unit of acceleration is meter /second2 and its dimensional formula is (LT–2). If the velocity of an object undergoes equal changes in equal interval of time, then its acceleration is said to be ‘uniform’. If the magnitude of the velocity (speed) of an object is increasing with time, then the acceleration of the object is positive. If the magnitude of the velocity (speed) is decreasing, then the acceleration is negative and it is called ‘retardation’.
Let a be the acceleration of the blocks m1 and m2, and T the tension in the cord, which is uniform throughout as the cord is massless and the pulley is frictionless. The force acting on the block m1 are: (i) its weight m1g which is the force exerted by the earth, (ii) the tension T in the string, and (iii) the normal force N exerted by the inclined surface (the force is normal because there is no frictional force between the surfaces). The net force on m1 along the plane is T-m1g sin θ, and that perpendicular to the plane is N – m1g cos θ.
17 ACCURACY AND ERRORS IN MEASUREMENT In many experiments in the physics laboratory, the aim is to determine the value of physical constant. To determine a physical constant, we have to measure the various quantities 26 Mechanics which are connected with that physical constant by a formula. For example, to determine the density (ρ) of a metal block, we have to measure its mass (m) and its volume (V) which are related to ρ by the formula: ρ = m/V The accuracy in the value of ρ obviously depends upon the accuracy in the measurements of m and V.
Mechanics by R.K. Shukla