The angle of projection for a range is equal to the distance through which the particle would have fallen in order to acquire a velocity equal to the velocity of projection, will be

The range of projectile on a downward inclined plane is ________ the range on upward inclined plane for the same velocity of projection and angle of projection.

A

Less than

B

More than

C

Equal to

D

None of these

For the given values of initial velocity of projection and angle of inclination of the plane, the maximum range for a projectile projected upwards will be obtained, if the angle of projection is

A

$$\alpha = \frac{\pi }{4} - \frac{\beta }{2}$$

B

$$\alpha = \frac{\pi }{2} + \frac{\beta }{2}$$

C

$$\alpha = \frac{\beta }{2} - \frac{\pi }{2}$$

D

$$\alpha = \frac{\pi }{4} - \frac{\beta }{4}$$

E

$$\alpha = \frac{\pi }{2} - \frac{\beta }{2}$$

The potential energy of a particle falling through a straight shaft drilled through the earth (assumed homogenous and spherical) is proportional to (where r is the distance of’the particle from centre of the earth)

A

log r

B

r

C

r²

D

$$\frac{1}{{\text{r}}}$$

The Cartesian equation of trajectory is (where u = Velocity of projection, $$\alpha $$ = Angle of projection and x, y = Co-ordinates of any point on the trajectory after t seconds.)

A

$${\text{y}} = \frac{{{\text{g}}{{\text{x}}^2}}}{{2{{\text{u}}^2}{{\cos }^2}\alpha }} + {\text{x}}\tan \alpha $$

B

$${\text{y}} = \frac{{{\text{g}}{{\text{x}}^2}}}{{2{{\text{u}}^2}{{\cos }^2}\alpha }} - {\text{x}}\tan \alpha $$

C

$${\text{y}} = {\text{x}}\tan \alpha - \frac{{{\text{g}}{{\text{x}}^2}}}{{2{{\text{u}}^2}{{\cos }^2}\alpha }}$$

D

$${\text{y}} = {\text{x}}\tan \alpha + \frac{{{\text{g}}{{\text{x}}^2}}}{{2{{\text{u}}^2}{{\cos }^2}\alpha }}$$

Sphericity is the ratio of the surface area of a spherical particle having the same volume as the particle to the surface area of the particle. Which of the following has the maximum value of sphericity?

A

Sphere

B

Cube

C

Cylinder (L/D = 1)

D

Raschig rings

One end of an elastic string of natural length / and modulus X is kept fixed while to the other end is attached a particle of mass m which is hanging freely under gravity. The particle is pulled down vertically through a distance x, held at rest and then released. The motion is

A

a simple harmonic motion

B

a rectilinear motion with constant speed

C

a damped oscillatory motion

D

none of the above

The range of projectile will be maximum for a given velocity of projectile, when the angle of projection ($$\alpha $$) is

A

$$\frac{\beta }{2}$$

B

30° + $$\frac{\beta }{2}$$

C

45° + $$\frac{\beta }{2}$$

D

60° + $$\frac{\beta }{2}$$

For a given velocity of a projectile, the range is maximum when the angle of projection is

A

30°

B

45°

C

90°

D

0°

A particle dropped from the top of a tower uniformly falls on ground at a distance which is equal to the height of tower. Which of the following paths will be traversed by the particle ?

A

Circle

B

Parabolic

C

Great circle

D

Hyper–parabolic

The velocity of a body fallen from height ‘h’, on reaching the ground is given by

A

v = 2gh

B

v = 2gh²

C

$${\text{v}} = \sqrt {2{\text{gh}}} $$

D

$${\text{v}} = \frac{1}{{\sqrt {2{\text{gh}}} }}$$

The angle of projection for a range is equal to the distance through which the particle would have fallen in order to acquire a velocity equal to the velocity of projection, will be

Related Questions