JEE Questions for Maths Statics And Dynamics Quiz 3

Two balls are projected from the same point in directions inclined at 45° and 60° to the horizontal, respectively. If they attain the same height, then the ratio of their velocities of projection is

0%
0%
3 :1
0%
3 : 2
0%

0%
15°
0%
30°
0%
45°
0%
60°

The product of two times of flight from a point P to another point Q with a given velocity of projection is

0%
0%
2)
0%
0%

A stone of mass m is thrown vertically upwards with a velocity of 9.8 ms^-1 . The height of the point, where KE = PE is (g = 9.8 ms^-2 )

0%
9.8 m
0%
4.9 m
0%
2.45 m
0%
2 m

A particle is projected from a point on the horizontal plane so as to just clear two walls each of height 20 m at distances 30 m and 170 m respectively from the point of projection. If α is the angle of projection, then

0%
40 tan α = 51
0%
40 cot α = 51
0%
30 tan α = 23
0%
30 cot α = 23

Two parabolic paths of angles α and β of projection aimed at a target on the horizontal plane through O, fall p units short and the other p units far from the target. If θ is the correct angle of projection so as to hit the target, then sin 2θ is equal to

0%
1/ 2 (tan α + tan β )
0%
1/ 2 (tan α - tan β )
0%
1/ 2 (sin 2α + sin 2β )
0%
1/ 2 (sin 2α - sin 2β )

A sphere S₁ impacting directly on an equal sphere S₂ at rest. If the coefficient of restitution is e, then the velocities of S₁ and S₂ are in the ratio

0%
0%
2)
0%
0%

Given that the force acting on a material point is inversely proportional to the velocity of the moving point. Then, the kinetic energy of the point is a........ function of time.

0%
exponential
0%
linear
0%
second degree
0%
non-linear

A particle of mass m is projected from a fixed point O into the air with velocity u in a direction making an angle α with the horizontal. Then, the motion of the particle describes a parabola with the latusrectum

0%
2 / g (horizontal velocity) 2
0%
2 / g (vertical velocity)
0%
0%

If a particle is projected with a velocity 49 m/s making an angle 60° with the horizontal, its time of flight is

0%
0%
2)
0%
0%
None of the above

A ball of mass 3 kg moving with a velocity of 3 m/s collides with another ball of mass 1 kg moving with velocity u in the opposite direction. If the first ball comes to rest after the impact and e = 2/ 7, then u (in m/s) is equal to

0%
0%
2)
0%
0%

A particle is projected from a point O with velocity u at an angle of 60° with the horizontal. When it is moving in a direction at right angle to its direction at O, then its velocity is given by

0%
0%
2)
0%
0%

Two masses are projected with equal velocity u at angles 30° and 60°, respectively. If the ranges covered by the masses are R₁ and R₂ , then

0%
R1 > R2
0%
R1 = R2
0%
R1 = 4R2
0%
R2 > R1

From a point on the ground at a distance 70 ft from the foot of a vertical wall, a ball is thrown at an angle of 45° which just clears the top of the wall and afterwards strikes the ground at a distance 30 ft on the other side of the wall. The height of the wall is

0%
20 ft
0%
21 ft
0%
10 ft
0%
105 ft

A ball is projected at an angle α . Its range will be maximum at an angle

0%
0
0%
2)
0%
0%
π

A force 2 units acts along the line x - 4 = y - 5. The moment of the force about the point (1,along Z-axis is

0%
0
0%
2)
0%
0%

The magnitude of the two forces forming a couple is 36 N each and the arm of the couple is 4 m. The magnitude of each force (in Newtons) of an equivalent couple, whose arm is 9 m, is

0%
18
0%
26
0%
16
0%
15

In a right angled ∆ABC , ∠ A = 90° and sides a, b, c are respectively, 5 cm, 4 cm and 3 cm. If a force F has moments 0, 9 and 16 (in N-cm) respectively about vertices A, B and C , then the magnitude of F is

0%
3
0%
4
0%
5
0%
9

Three forces A, B and C acting at a point are in equilibrium. The ratio of angles between A and B, B and C, A and C is 1 : 2 : 3 .Then , A : B : C is equal to