What is the distance of the particle from the origin at time 2 s?
[ Take αb and αs (αb > αs) to be the thermal expansion coefficients of brass and steel respectively. Consider the thickness of each bar is initially t which is very small. ]
The position vector of a particle R as a function of time is given by
where R is in metres, t is in seconds and i and j denote unit vectors along x and y directions, respectively. Which one of the following statements is wrong for the motion of particle?
(Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 m s-2). (The figures are schematic and not drawn to scale)
The relation between H, u and n is
(2 m, 3 m) at time t = 0,
(6 m, 7 m) at time t = 2 s and
(13 m, 14 m) at time t = 5 s
Average velocity vector from t = 0 to t = 5 s is:
|List I||List II|
|P.||Lift is accelerating vertically up.||1.||d = 1.2 m|
|Q.||Lift is accelerating vertically down with an acceleration less than the gravitational acceleration.||2.||d > 1.2 m|
|R.||Lift is moving vertically up with constant speed.||3.||d < 1.2 m|
|S.||Lift is falling freely.||4.||No water leaks out of the jar.|
A projectile is given an initial velocity of , where is along the ground and is along the vertical. If g = 10 m/s2, the equation of its trajectory is:
A particle of mass m is projected from the ground with an initial speed u0 at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is
A stone falls freely under gravity. It covers distances h1, h2 and h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h1, h2 and h3 is:
Reason The two acceleration are perpendicular to each other.
Reason: The body will be momentarily at rest when it reverses its direction of motion.
Reason: Horizontal velocity has no effect on the vertical direction.
Reason In uniform circular motion the magnitude of acceleration remains constant but the direction continuously changes.
A small block is connected to one end of a mass less spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at . It then executes simple harmonic motion with angular frequency rad/s. Simultaneously at, a small pebble is projected with speed v from point P at an angle of as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at s, the value of v is (take)
The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectiles is :
Consider a disc rotating in the horizontal plane will a constant angular speedabout its centre O. The disc has shaded region n one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed (1/8) rotation, (ii) their range is less than half the disc, and (iii) remains constant throughout. Then
Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed . The discs are in the same horizontal plane. At time, the pints P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is in one time period (T) of rotation of the discs, as a function of time is best represented by
The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed and (ii) and inner disc of radius 2R rotating anti-clockwise the angular speed. The ring and disc are separated by frictionless ball bearing. The system is in the x-z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of with horizontal. Then with respect to the horizontal surface,
Reason: At the highest point only one component of velocity present.
A train is moving along a straight line with a constant acceleration ‘a’. A body standing in the train throws a ball forward with a speed of, at an angle of to the horizontal. The boy has to move forward by 1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in is
Reason: Velocity is a vector quantity and speed is a scalar quantity.
s = 6t2 − t3
The time in seconds at which the particle will attain zero velocity again is
If the resultant of all external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that
Reason The path of a projectile is independent of the gravitational force of earth.
A piece of wire is bent in the shape of a parabola (y-axis vertical) with a bead of mass on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration The distance of the new equilibrium position of the bead, where the bend can stay at rest with respect to the wire, from the y-axis is
For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.
STATEMENT − 2
If the observer and the object are moving at velocities and respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is .
Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graph given in Column II. Indicate your answer by darkening the appropriate bubbles of the matrix given in the ORS.
|Column I||Column II|
Potential energy of a simple pendulum(y axis) as a function of displacement (x axis)
Displacement (y axis) as a function of time (x axis) for a one dimensional motion at zero or constant acceleration when the body is moving along the positive x − direction
Range of a projectile (y axis) as a function of its velocity (x axis) when projected at a fixed angle
The square of the time period (y axis) of a simple pendulum as a function of its length (x axis)
(A) 110 m/s
(B) 55 m/s
(C) 550 m/s
(D) 660 m/s