If vectors A=cos wti + sin wtj and B= cos wt/2 i + sin wt/2 j are functions of time,
If vectors A=cos wti + sin wtj and B= cos wt/2 i + sin wt/2 j are functions of time, then the value of t at which they are orthogonal to each other is
Motion in Plane
The position vector of a particle R as a function of time is given by
The position vector of a particle R as a function of time is given by R=4sin(2πt)i + 4 cos (2πt) j, where R is in meter, t in seconds and i and j denote unit […]
A ship A is moving westwards with a speed of 10 km/h and a ship B 100 km
A ship A is moving westwards with a speed of 10 km/h and a ship B 100 km South of A is moving Northwards with a speed of 10 km/h. The time after which the […]
The angle between the vectors (i+j) and (j+k) is
The angle between the vectors (i+j) and (j+k) is
Options
(a) 90⁰ (b) 60⁰ (c) 30⁰ (d) 45⁰
Correct Answer:
60⁰
Explanation:
A = i + j, B = j + k
A . […]
For a given velocity, a projectile has the same range R for two angles of projection.
For a given velocity, a projectile has the same range R for two angles of projection. If t₁ and t₂ are the times of flight in the two cases, then
Options
(a) t₁t₂ […]
A proton of mass 1.6×10⁻²⁷ kg goes round in a circular orbit of radius 0.10 m under
A proton of mass 1.6×10⁻²⁷ kg goes round in a circular orbit of radius 0.10 m under a centripetal force of 4×10⁻¹³ N. The frequency of revolution of the proton is about
Options
In a uniform circular motion,
In a uniform circular motion,
Options
(a) Velocity and acceleration remain constant (b) Kinetic energy remains constant (c) Speed and acceleration change (d) Only velocity changes, acceleration remains constant
Correct Answer:
Kinetic energy […]
The circular motion of a particle with constant speed is
The circular motion of a particle with constant speed is
Options
(a) Periodic but not simple harmonic (b) Simple harmonic but not periodic (c) Period and simple harmonic (d) Neither periodic not simple harmonic
The equations of motion of a projectile are given by x=36 t metre and 2y=96t-9.8t²
The equations of motion of a projectile are given by x=36 t metre and 2y=96t-9.8t² metre. The angle of projection is
Options
(a) sin⁻¹ (4/5) (b) sin⁻¹ (3/5) (c) sin⁻¹ (4/3) (d) sin⁻¹ (3/4)
The coefficient of friction between the tyres and the road is 0.25. The maximum speed
The coefficient of friction between the tyres and the road is 0.25. The maximum speed with which a car can be driven round a curve of radius 40 m without skidding is (assume g=10 ms⁻²) […]