Two objects are projected at angles 30° and 60° respectively with respect to the horizontal direction. The range of two objects are denoted as R_30° and R_30°. Choose the correct relation from the following

(a)

R_30° = R_60°

(b)

R_30° = 4R_60°

(c)

R_30° =\(\frac{R_{60°}}{2}\)

(d)

R_30° = 2R_60°

Force acting on the particle moving with constant speed is

(a)

always zero

(b)

need not be zero

(c)

always non zero

(d)

cannot be concluded

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

(a)

v

(b)

v²

(c)

v³

(d)

v⁴

Two discs of same moment of inertia rotating about their regular axis passing through center and perpendicular to the plane of the disc with angular velocities ω₁ and ω₁. They are brought in to contact face to face coinciding with the axis of rotation. The expression for loss of energy during this process is

(a)

\(\frac{1}{4}\)\(I(\omega _{1}-\omega _{2})^2\)

(b)

\(I(\omega _{ 1 }-\omega _{ 2 })^{ 2 }\)

(c)

\(\frac{1}{8}\)\(I(\omega _{1}-\omega _{2})^2\)

(d)

\(\frac{1}{2}I\)\((\omega _{1}-\omega _{2})^2\)

The work done by the Sun’s gravitational force on the Earth is

(a)

always zero

(b)

always positive

(c)

can be positive or negative

(d)

always negative

A certain number of spherical drops of a liquid of radius R coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

(a)

energy = 4 V T \(\left( \frac { 1 }{ r } -\frac { 1 }{ R } \right) \)is released

(b)

energy = 3 V T \(\left( \frac { 1 }{ r } +\frac { 1 }{ R } \right) \)is absorbed

(c)

energy = 3 V T \(\left( \frac { 1 }{ r } -\frac { 1 }{ R } \right) \)is released

(d)

energy is neither released nor absorbed

In an isochoric process, we have

(a)

W = 0

(b)

Q = 0

(c)

ΔU = 0

(d)

ΔT = 0

If s_P and s_V denote the specific heats of nitrogen gas per unit mass at constant pressure and constant volume respectively, then

(a)

s_P - s_V = 28R

(b)

s_P - s_V = R/28

(c)

s_P - s_V = R/14

(d)

s_P - s_V = R

An ideal spring of spring constant k, is suspended from the ceiling of a room and a block of mass M is fastened to its lower end. If the block is released when the spring is un-stretched, then the maximum extension in the spring is

(a)

4\(\frac { Mg }{ k } \)

(b)

\(\frac { Mg }{ k } \)

(c)

2\(\frac { Mg }{ k } \)

(d)

\(\frac { Mg }{ 2k } \)

Which of the following represents a wave

(a)

(x - vt)³

(b)

x(x+vt)

(c)

\(\frac{1}{x+vt}\)

(d)

sin(x+vt)