Physics and Mathematics Physics - Physics and Mathematics

A vector is not changed if:

1. It is rotated through an arbitrary angle.
2. It is multiplied by an arbitrary scalar.
3. It is cross multiplied by a unit vector.
4. It is slid parallel to itself.

The x-component of the resultant of several vectors:

1. Is equal to the sum of the x-components of the vectors.
2. May be smaller than the sum of the magnitudes of the vectors.
3. May be greater than the sum of the magnitudes of the vectors.
4. May be equal to the sum of the magnitudes of the vectors.

Which of the sets given below may represent the magnitudes of three vectors adding to zero?

1. 2, 4, 8
2. 4, 8, 16
3. 1, 2, 1
4. 0.5, 1, 2

A situation may be described by using different sets of coordinate axes having different orientations. Which of the following do not depend on the orientation of the axes?

1. The value of a scalar.
2. Component of a vector.
3. A vector.
4. The magnitude of a vector.

Is a vector necessarily changed if it is rotated through an angle?

The length of the string of a simple pendulum is measured with a metre scale to be 90.0cm. The radius of the bob plus the length of the hook is calculated to be 2.13cm using measurements with a slide callipers. What is the effective length of the pendulum? (The effective length is defined as the distance between the point of suspension and the centre of the bob.)

Can we have physical quantities having magnitude and direction which are not vectors?

The length and the radius of a cylinder measured with a slide callipers are found to be 4.54cm and 1.75cm respectively. Calculate the volume of the cylinder.

A mosquito net over a 7ft × 4ft bed is 3ft high. The net has a hole at one corner of the bed through which a mosquito enters the net. It flies and sits at the diagonally opposite upper corner of the net.

1. Find the magnitude of the displacement of the mosquito.
2. Taking the hole as the origin, the length of the bed as the X-axis, its width as the Y-axis, and vertically up as the Z-axis, write the components of the displacement vector.

A carrom board (4ft × 4ft square) has the queen at the centre. The queen, hit by the striker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen:

1. From the centre to the front edge.
2. From the front edge to the hole.
3. From the centre to the hole.

The thickness of a glass plate is measured to be 2.17mm, 2.17mm and 2.18mm at three different places. Find the average thickness of the plate from this data.

A spy report about a suspected car reads as follows. "The car moved 2.00km towards east, made a perpendicular left turn, ran for 500m, made a perpendicular right turn, ran for 4.00km and stopped". Find the displacement of the car.