Which of the following pairs of physical quantities have same dimension?

(a)

force and power

(b)

torque and energy

(c)

torque and power

(d)

force and torque

The fractional error \(\left( {{\triangle x}\over{x}} \right)\)  _____________.

(a)

\(\pm\left( {{\triangle x}\over{x}} \right)\)

(b)

\(\pm n\left( {{\triangle a}\over{a}}\right)\)

(c)

\(\pm n \log_e \left( {{\triangle a}\over{a}}\right)\)

(d)

\(\pm n \log_{10}{{\triangle a}\over{a}}\)

Ihe density of a cube is measured by measuring its mass and length of its side. If the maximum error in the measurement of mass and length are 3% and 2% respectively, the maximum error in the measurement of density is ________________.

(a)

1%

(b)

9%

(c)

7%

(d)

5%

The numbers 3.665 and 3.635 on rounding off to 3 significant figures will give____________

(a)

3.66 and 3.63

(b)

3.66 and 3.64

(c)

3.67 and 3.63

(d)

3.67 and 3.64

Which of the following statements is/are not true?

(a)

v, a and s are vectors

(b)

Mass, energy, work are vectors

(c)

Vector has only magnitude whereas scalar has both magnitude and direction

(d)

both (b) and (c)

It is found that \(\left|A+B\right|=\left|A\right|.\) This necessarily implies ____________.

(a)

B = 0

(b)

A, B are anti-parallel

(c)

A, B are perpendicular

(d)

\(A,B\le 0\)

The expression for maximum height attained when the body is projected at an angle with the horizontal is:

(a)

\(\frac{u\sin\theta}{2g}\)

(b)

\(\frac{u\sin^2\theta}{2g}\)

(c)

\(\frac{u^2\sin^2\theta}{g}\)

(d)

\(\frac{u^2\sin^2\theta}{2g}\)

A body moving with a constant speed v in a circle of radius r. Its angular acceleration is ______________

(a)

0

(b)

vr

(c)

\(\frac{v}{r}\)

(d)

\(\frac{v^2}{r}\)

1 radian = ________.

(a)

50729°

(b)

572.9°

(c)

\(\frac{\pi}{180}\)

(d)

57.295°

Vectors can be added _____________

(a)

algebrically

(b)

geometrically

(c)

graphically

(d)

both (b) and (c)

Which of the following curve does not represent motion in one dimension?

(a)

(b)

(c)

(d)

A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q separated by a distance with velocity 30 km/h and 40 km/h respectively. The velocity of the car midway between P and Q is ______________.

(a)

33.3km/h

(b)

20\(\sqrt{2}\) km/h

(c)

25\(\sqrt{2}\)km/h

(d)

35km/h

If an object executes a to and fro motion about a fixed point, is an example for ____________.

(a)

rotational motion

(b)

vibratory motion

(c)

circular motion

(d)

curvilinear motion

Which of the following is not a scalar?

(a)

Volume

(b)

angular momentum

(c)

Relative density

(d)

time

A unit vector is used to specify ______________.

(a)

only magnitude

(b)

only direction

(c)

either magnitude (or) direction

(d)

absolute value

The resultant of \(\vec A+\vec B\) acts along x-axis. If A = \(2\hat i-3\hat j+2\hat k\) then B is __________.

(a)

\(-2\hat i+\hat j+\hat k\)

(b)

\(3\hat j-2\hat k\)

(c)

\(-2\hat i-3\hat j\)

(d)

\(-2\hat i-2\hat k\)

The vectors \(\vec A\) and \(\vec B\) to be mutually orthogonal when _________.

(a)

\(\vec A+\vec B=0\)

(b)

\(\vec A-\vec B=0\)

(c)

\(\vec A.\vec B=0\)

(d)

\(\vec A\times \vec B=0\)

\(|\vec A\times \vec B|\) is equal to ________________

(a)

\(-|\vec A\times \vec B|\)

(b)

\(|\vec B\times \vec A|\)

(c)

\(-|\vec B\times \vec A|\)

(d)

\(\frac{\vec A\times \vec B}{|\vec A\times \vec B|}\)

If two vectors \(\vec A\) and \(\vec B\) form adjacent sides of parallelogram, then the magnitude of \(|\vec A\times \vec B|\) will give _______ of parallelogram.

(a)

length

(b)

area

(c)

volume

(d)

diagonal

If a body moving in a circular path with uniform speed, then _____________.

(a)

the acceleration is directed towards its centre

(b)

velocity and acceleration are perpendicular to each other

(c)

speed of the body is constant but its velocity is varying.

(d)

all the above

Choose appropriate free body diagram for the particle experiencing net acceleration along negative y direction. (Each arrow mark represents the force acting on the system).

(a)

(b)

(c)

(d)

If a person moving from pole to equator, the centrifugal force acting on him

(a)

increases

(b)

decreases

(c)

remains the same

(d)

increases and then decreases

If the linear momentum of the object is increased by 0.1% then the kinetic energy is Increased by

(a)

0.1 %

(b)

0.2 %

(c)

0.4 %

(d)

0.01 %

A disc of the moment of inertia I_a is rotating in a horizontal plane about its symmetry axis with a constant angular speed \(\omega\). Another disc initially at rest of moment of inertia I_b is dropped coaxially on to the rotating disc. Then, both the discs rotate with the same constant angular speed. The loss of kinetic energy due to friction in this process is,

(a)

\(\frac { 1 }{ 2 } \frac { { I }_{ b }^{ 2 } }{ 2({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(b)

\(\frac { { I }_{ b }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(c)

\(\frac { { ({ I }_{ b }-{ I }_{ a }) }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(d)

\(\frac { 1 }{ 2 } \frac { { { I }_{ b }{ I }_{ b } } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

The kinetic energy of the satellite orbiting around the Earth is

(a)

equal to potential energy

(b)

less than potential energy

(c)

greater than kinetic energy

(d)

zero