Science (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the x-t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.

Read the statement below carefully and state, with reason and example, if it is true or false:

A particle in one-dimensional motion with zero speed at an instant may have non-zero acceleration at that instant

Explain clearly, with examples, the distinction between:

1. magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval.
2. magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign true ? [For simplicity, consider one-dimensional motion only].

Look at the graph carefully and state, with reason, that this cannot possibly represent the one-dimensional motion of a particle.

Rain is falling vertically with a speed of 30 m s^–1. A woman rides a bicycle with a speed of 10 m s^–1in the north to south direction. What is the direction in which she should hold her umbrella?

A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s^–1 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m s^–2).

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s^–1. What is the trajectory of the bob if the string is cut when the bob is

1. At one of its extreme positions,
2. At its mean position.

A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and why?

Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by `v^2 = (2gh)/((1+k^2"/"R^2))`.

Using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.

Read each statement below carefully, and state, with reasons, if it is true or false;

The instantaneous speed of the point of contact during rolling is zero.

Read each statement below carefully, and state, with reasons, if it is true or false;

For perfect rolling motion, work done against friction is zero.

Read each statement below carefully, and state, with reasons, if it is true or false;

A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling) motion

Can an object be in pure translation as well as in pure rotation?

Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping, ___________ .

A hollow sphere and a solid sphere having same mss and same radii are rolled down a rough inclined plane.

A sphere cannot roll on

In rear-wheel drive cars, the engine rotates the rear wheels and the front wheels rotate only because the car moves. If such a car accelerates on a horizontal road the friction

(a) on the rear wheels is in the forward direction

(b) on the front wheels is in the backward direction

(c) on the rear wheels has larger magnitude than the friction on the front wheels

(d) on the car is in the backward direction.

A sphere can roll on a surface inclined at an angle θ if the friction coefficient is more than \[\frac{2}{7}g \tan\theta.\] Suppose the friction coefficient is \[\frac{1}{7}g\ tan\theta.\] If a sphere is released from rest on the incline, _____________ .

The following figure shows a smooth inclined plane fixed in a car accelerating on a horizontal road. The angle of incline θ is related to the acceleration a of the car as a = g tanθ. If the sphere is set in pure rolling on the incline, _____________.

To construct a barometer, a tube of length 1 m is filled completely with mercury and is inverted in a mercury cup. The barometer reading on a particular day is 76 cm. Suppose a 1 m tube is filled with mercury up to 76 cm and then closed by a cork. It is inverted in a mercury cup and the cork is removed. The height of mercury column in the tube over the surface in the cup will be