The physical quantity that has the same dimensional formula as pressure is:
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If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.
If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of
Taking into account of the significant figures, what is the value of 9.99m − 0.0099m?
The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (n-1) divisions of main scale. The least count of the vernier callipers is,
A physical quantity of the dimensions of length that can be formed out of c, G and is [c is velocity of light, G is the universal constant of gravitation and e is charge].
If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as [ηxρyγz] where η, ρ and γ are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by.
In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows
The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are
The density of a material in CGS system of units is 4g∕cm3 In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be
A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is
If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be
Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be
The ratio of the distances travelled by a freely falling body in the 1st ,2nd ,3rd and 4th second
A car starts from rest and accelerates at 5 m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s?(Take g = 10 m/s2)[NEET
Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be
Two cars P and Q start from a point at the same time in a straight line and their positions are represented by xp(t) = (at + bt2) and xQ(t) = (ft − t2). At what time do the cars have the same velocity?
A stone falls freely under gravity. It covers distances h1, h2 and h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h1 and h2 and h3 is
The motion of a particle along a straight line is described by equation x = 8 + 12t − t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is
A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is
A ball is dropped from a high rise platform at 1 = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18 s. What is the value of v?
(Take g = 10m∕s2)
A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S1 and that covered in the first 20 seconds is S2, then
A ball is projected with a velocity, 10ms−1, at an angle of 60∘ with the vertical direction. Its speed at the highest point of its trajectory will be
The speed of a swimmer in still water is 20m∕s. The speed of river water is 10m/s and is flowing due east.
If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given by
Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed vA and vB respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be
The x and y coordinates of the particle at any time are x = 5t − 2t2 and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s
If vectors are functions of time, then the value of t at which they are orthogonal to each other is