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

A lift is coming from 8^th floor and is just about to reach 4^th floor. Taking ground floor as origin and positive direction upwards for all quantities, which one of the following is correct?

A graph of x versus t is shown in figure. Choose correct alternatives from below.

1. The particle was released from rest at t = 0.
2. At B, the acceleration a > 0.
3. At C, the velocity and the acceleration vanish.
4. Average velocity for the motion between A and D is positive.
5. The speed at D exceeds that at E.

Give example of a motion where x > 0, v < 0, a > 0 at a particular instant.

An object falling through a fluid is observed to have acceleration given by a = g – bv where g = gravitational acceleration and b is constant. After a long time of release, it is observed to fall with constant speed. What must be the value of constant speed?

In a two dimensional motion, instantaneous speed v₀ is a positive constant. Then which of the following are necessarily true?

In a two dimensional motion, instantaneous speed v0 is a positive constant. Then which of the following are necessarily true?

Motion in two dimensions, in a plane can be studied by expressing position, velocity and acceleration as vectors in cartesian co-ordinates A = `A_xhati + A_yhatj` where `hati` and `hatj` are unit vector along x and y directions, respectively and Ax and Ay are corresponding components of (Figure). Motion can also be studied by expressing vectors in circular polar co-ordinates as A = `A_rhatr + A_θhatθ` where `hatr = r/r = cos θhati + sin θj` and `hatθ = - sin  θhati + cos θ hatj` are unit vectors along direction in which `r` and `θ` are increasing.

1. Express `hati` and `hatj` in terms of `hatr` and `hatθ`
2. Show that both `hatr` and `hatθ` are unit vectors and are perpendicular to each other.
3. Show that `d/(dt) (hatr) = ωhatθ` where `θ = (dθ)/(dt)` and `d/(dt) (hatθ) = - ωhatr`
4. For a particle moving along a spiral given by `t = aθhatr`, where a = 1 (unit), find dimensions of ‘a’.
5. Find velocity and acceleration in polar vector representation for particle moving along spiral described in (d) above.

Two billiard balls A and B, each of mass 50 g and moving in opposite directions with speed of 5 ms^–1 each, collide and rebound with the same speed. If the collision lasts for 10^–3 s, which of the following statements are true?

1. The impulse imparted to each ball is 0.25 kg ms^–1 and the force on each ball is 250 N.
2. The impulse imparted to each ball is 0.25 kg ms^–1 and the force exerted on each ball is 25 × 10^–5 N.
3. The impulse imparted to each ball is 0.5 Ns.
4. The impulse and the force on each ball are equal in magnitude and opposite in direction.

A girl riding a bicycle along a straight road with a speed of 5 ms^–1 throws a stone of mass 0.5 kg which has a speed of 15 ms^–1 with respect to the ground along her direction of motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown? What is the change in speed, if so?

A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. Find the recoil velocity of the gun. (acceleration due to gravity = 10 ms^–2)

The variation of angular position θ, of a point on a rotating rigid body, with time t is shown in figure. Is the body rotating clock-wise or anti-clockwise?

Two cylindrical hollow drums of radii R and 2R, and of a common height h, are rotating with angular velocities ω(anti-clockwise) and ω(clockwise), respectively. Their axes, fixed are parallel and in a horizontal plane separated by (3R + δ). They are now brought in contact (δ → 0).

1. Show the frictional forces just after contact.
2. Identify forces and torques external to the system just after contact.
3. What would be the ratio of final angular velocities when friction ceases?

The temperature of a wire is doubled. The Young’s modulus of elasticity ______.

The temperature of a wire is doubled. The Young’s modulus of elasticity ______.

A rigid bar of mass M is supported symmetrically by three wires each of length l. Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to ______.

The Young’s modulus for steel is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress?

Identical springs of steel and copper are equally stretched. On which, more work will have to be done?

What is the Young’s modulus for a perfect rigid body ?

A steel rod (Y = 2.0 × 10¹¹ Nm^–2; and α = 10^–50 C^–1) of length 1 m and area of cross-section 1 cm² is heated from 0°C to 200°C, without being allowed to extend or bend. What is the tension produced in the rod?

A truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 5 mm. When the car just begins to move, the tension in the cable is 800 N. How much has the cable stretched? (Young’s modulus for steel is 2 × 10¹¹ Nm^–2.)