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

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.)

A steel wire of mass µ per unit length with a circular cross section has a radius of 0.1 cm. The wire is of length 10 m when measured lying horizontal, and hangs from a hook on the wall. A mass of 25 kg is hung from the free end of the wire. Assuming the wire to be uniform and lateral strains << longitudinal strains, find the extension in the length of the wire. The density of steel is 7860 kg m^–3 (Young’s modules Y = 2 × 1011 Nm^–2).

If the yield strength of steel is 2.5 × 10⁸ Nm^–2, what is the maximum weight that can be hung at the lower end of the wire?

A steel rod of length 2l, cross sectional area A and mass M is set rotating in a horizontal plane about an axis passing through the centre. If Y is the Young’s modulus for steel, find the extension in the length of the rod. (Assume the rod is uniform.)

In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus the vertical through the centre of gravity does not fall within the base. The elastic torque caused because of this bending about the central axis of the tree is given by `(Ypir^4)/(4R) . Y` is the Young’s modulus, r is the radius of the trunk and R is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.

In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus the vertical through the centre of gravity does not fall within the base. The elastic torque caused because of this bending about the central axis of the tree is given by `(Ypir^4)/(4R) . Y` is the Young’s modulus, r is the radius of the trunk and R is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.