and , then angle between vectors A and B is:
(1)
(2)
(3)
(4)
If vectors \(\overrightarrow{{A}}=\cos \omega t \hat{{i}}+\sin \omega t \hat{j}\) and \(\overrightarrow{{B}}=\cos \left(\frac{\omega t}{2}\right)\hat{{i}}+\sin \left(\frac{\omega t}{2}\right) \hat{j}\) are functions of time. Then, at what value of \(t\) are they orthogonal to one another?
1. \(t = \frac{\pi}{4\omega}\)
2. \(t = \frac{\pi}{2\omega}\)
3. \(t = \frac{\pi}{\omega}\)
4. \(t = 0\)
Six vectors through have the magnitudes and directions indicated in the figure. Which of the following statements is true?
1.
2.
3.
4.
and are two vectors and θ is the angle between them. If , then the value of θ will be:
1. 60o
2. 45o
3. 30o
4. 90o
If a curve is governed by the equation y=sinx, then the area enclosed by the curve and x-axis between x =0 and x = is (shaded region) :
1. 1 unit
2. 2 units
3. 3 units
4. 4 units
The acceleration of a particle starting from rest varies with time according to relation, . The velocity of the particle at time instant t is: (\(Here, a=\frac{dv}{dt}\))
1.
2.
3.
4.
The displacement of the particle is zero at t=0 and at t=t it is x. It starts moving in the x-direction with a velocity that varies as , where k is constant. The velocity will : (Here, \(v=\frac{dx}{dt}\))
1. vary with time.
2. be independent of time.
3. be inversely proportional to time.
4. be inversely proportional to acceleration.
The acceleration of a particle is given as . At t = 0, v = 0 and x = 0. It can then be concluded that the velocity at t = 2 sec will be: (Here, \(a=v\frac{dv}{dx}\))
1. 0.05 m/s
2. 0.5 m/s
3. 5 m/s
4. 50 m/s
The acceleration of a particle is given by a=3t at t=0, v=0, x=0. The velocity and displacement at t = 2 sec will be: (\(Here, a=\frac{dv}{dt}~ and~v=\frac{dx}{dt}\))
1. 6 m/s, 4 m
2. 4 m/s, 6 m
3. 3 m/s, 2 m
4. 2 m/s, 3 m
The 9 kg block is moving to the right with a velocity of 0.6 m/s on a horizontal surface when a force F, whose time variation is shown in the graph, is applied to it at time t = 0. Calculate the velocity v of the block when t= 0.4s. The coefficient of kinetic fricton is . [This question includes concepts from Work, Energy & Power chapter]
1. 0.6 m/s
2. 1.2 m/s
3. 1.8 m/s
4. 2.4 m/s