The ratio of the ranges on the inclined plane with motion upward and with motion downward for a given velocity, angle 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

The time of flight (t) of a projectile on an upward inclined plane is
(where u = Velocity of projection, $$\alpha $$ = Angle of projection and $$\beta $$ = Inclination of the plane with the horizontal.)

A

$${\text{t}} = \frac{{{\text{g}}\cos \beta }}{{2{\text{u}}\sin \left( {\alpha - \beta } \right)}}$$

B

$${\text{t}} = \frac{{2{\text{u}}\sin \left( {\alpha - \beta } \right)}}{{{\text{g}}\cos \beta }}$$

C

$${\text{t}} = \frac{{{\text{g}}\cos \beta }}{{2{\text{u}}\sin \left( {\alpha + \beta } \right)}}$$

D

$${\text{t}} = \frac{{2{\text{u}}\sin \left( {\alpha + \beta } \right)}}{{{\text{g}}\cos \beta }}$$

If the angle of projection is double the angle of inclination ($$\alpha $$) of the plane on which particle is projected, the ratio of times of flight up the inclined plane and down the inclined plane, will be

A

$$\frac{1}{2}\,\cos \alpha $$

B

$$\frac{1}{2}\,\sin \alpha $$

C

$$\frac{1}{2}\,\tan \alpha $$

D

$$2\cos \alpha $$

The velocity ratio in case of an inclined plane inclined at angle 'θ' to the horizontal and weight being pulled up the inclined plane by vertical effort is

A

sinθ

B

cosθ

C

tanθ

D

cosecθ

In _________ the parallel projection rays are not perpendicular to the viewing plane as with orthographic projection, but strike the projection plane at an angle other than ninety degrees.

A

isometric projections

B

orthographic projections

C

axonometric projection

D

oblique projections

If the direction of projection bisects the angle between the vertical and the inclined plane, then the range of projectile on the inclined plane is

A

Zero

B

Maximum

C

Minimum

D

None of these

The direction of projection should bisect the angle between the inclined plane and the vertical for a range of a projectile on inclined plane

A

To be zero

B

To be maximum

C

To be minimum

D

None of these

A body of weight w placed on an inclined plane is acted upon by a force P parallel to the plane which causes the body just to move up the plane. If the angle of inclination of the plane is $$\theta $$ and angle of friction is $$\varphi $$, the minimum value of P, is

A

$$\frac{{{\text{w}}\sin \left( {\varphi - \theta } \right)}}{{\cos \varphi }}$$

B

$$\frac{{{\text{w}}\sin \left( {\theta - \varphi } \right)}}{{\cos \varphi }}$$

C

$$\frac{{{\text{w}}\cos \left( {\theta + \varphi } \right)}}{{\cos \varphi }}$$

D

$$\frac{{{\text{w}}\sin \theta \cos\left( {\theta - \varphi } \right)}}{{\sin\varphi }}$$

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

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

Two particles have been projected at angles 64° and 45° to the horizontal. If the velocity of projection of first is 10 m/sec, the velocity of projection of the other for equal horizontal ranges is

A

9.3 m/sec

B

8.3 m/sec

C

7.3 m/sec

D

6.3 m/sec

The ratio of the ranges on the inclined plane with motion upward and with motion downward for a given velocity, angle of projection will be

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