At what angle must the two forces (x + y) and (x – y) act so that the resultant comes out to be ?
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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
If vector and are functions of time, then the value of t at which they are orthogonal to each other will be:
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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 \(\vec{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?
1. \(x\vec{a}\) is a vector in the direction of \(\vec{a}\)
2. \(x\vec{a}\) is a vector collinear to \(\vec{a}\)
3. \(x\vec{a}\) and \(\vec{a}\) have independent directions
4. \(x\vec{a}\) is a vector perpendicular to \(\vec{a}\)
A body is moving according to the equation where x represents displacement and a, b and c are constants. The acceleration of the body is: (\(Given: a=\frac{d^2x}{dt^2}\))
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The linear velocity of a rotating body is given by , where is the angular velocity and r is the radius vector. The angular velocity of a body, and their radius vector is will be:
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A child pulls a box with a force of at an angle of above the horizontal. Then the horizontal
and vertical components of the force will be:
1. 100 N, 175 N
2. 86.6 N, 100 N
3. 100 N, 86.6 N
4. 100 N, 0 N
In the given figure
1. Angle between and is
2. Angle between and is
3. Angle between and is
4. Angle between and is