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

A $$\frac{{\sin \left( {\alpha + \beta } \right)}}{{\sin \left( {\alpha - \beta } \right)}}$$
B $$\frac{{\sin \left( {\alpha - \beta } \right)}}{{\sin \left( {\alpha + \beta } \right)}}$$
C $$\frac{{\cos \left( {\alpha - \beta } \right)}}{{\cos \left( {\alpha + \beta } \right)}}$$
D $$\frac{{\tan \left( {\alpha - \beta } \right)}}{{\tan \left( {\alpha + \beta } \right)}}$$

Correct Answer: $$\frac{{\sin \left( {\alpha - \beta } \right)}}{{\sin \left( {\alpha + \beta } \right)}}$$

Bissoy MCQ
#Civil Engineering #Applied Mechanics And Graphic Statics

Related Questions

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 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
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
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 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
A [[[
A body of weight 'W' is required to move up on rough inclined plane whose angle of inclination with the horizontal is 'α'. The effort applied parallel to the plane is given by (where μ = tanφ = Coefficient of friction between the plane and the body.)
A P = W tanα
B P = W tan (α + φ)
C P = W (sinα + μcosα)
D P = W (cosα + μsinα)
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 $${\text{y}} = {\text{x}}\tan \alpha + \frac{{{\text{g}}{{\text{x}}^2}}}{{2{{\text{u}}^2}{{\cos }^2}\alpha }}$$
The force required to move the body up the plane will be minimum if it makes an angle with the inclined plane __________ the angle of friction.
A Equal to
B Less than
C Greater than
D None of these
A body will begin to move down an inclined plane, if the angle of inclination of the plane is ________ the angle of friction.
A Equal to
B Less than
C Greater than
D None of these

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