Class 11th

Two balls of same mass and carrying equal charge are hung by threads of length $l$ from a fixed support. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, $x$ between the balls is proportional to:

(a.) $l$

(b.) $l^2$

(c.) $l^{2/3}$

(d.) $l^{1/3}$

Based on the passage, which of the following best captures the meaning of HIF, or hypoxia-inducible factor?

A. It is a protein that increases inside the cell when the oxygen levels fall, helping the cell survive.
B. It inhibits oxygen carrying process in the body as the oxygen level increases inside the cell.
C. It enables cells to adapt quickly to the changing environment and helps in its survival.
D. It regulates the amount of oxygen available to the cell and the body during exercise.

Based on the passage, which of the following best captures the meaning of HIF, or hypoxia-inducible factor?

A. It is a protein that increases inside the cell when the oxygen levels fall, helping the cell survive.
B. It inhibits oxygen carrying process in the body as the oxygen level increases inside the cell.
C. It enables cells to adapt quickly to the changing environment and helps in its survival.
D. It regulates the amount of oxygen available to the cell and the body during exercise.

Based on the passage, which of the following best captures the meaning of HIF, or hypoxia-inducible factor?

A. It is a protein that increases inside the cell when the oxygen levels fall, helping the cell survive.
B. It inhibits oxygen carrying process in the body as the oxygen level increases inside the cell.
C. It enables cells to adapt quickly to the changing environment and helps in its survival.
D. It regulates the amount of oxygen available to the cell and the body during exercise.

With reference to Fig. of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.)

(a) The moment of inertia of cube about z-axis is I_z = I_x + I_y

(b) The moment of inertia of cube about z′ is I_z =I_z +ma²/2

(c) The moment of inertia of cube about z″ is I_z+ma²/2 (d) I_x = I_y

Figure 7.5 shows a lamina in x-y plane. Two axes z and z′ pass perpendicular to its plane. A force F acts in the plane of lamina at point P as shown. Which of the following are true? (The point P is closer to z′-axis than the z-axis.)

(a) Torque τ caused by F about z axis is along ˆ -k.

(b) Torque τ′ caused by F about z′ axis is along ˆ -k.

(c) Torque τ caused by F about z axis is greater in magnitude than that about z axis.

(d) Total torque is given be τ = τ + τ′.

The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it ?

(a) The forces may be acting radially from a point on the axis.

(b) The forces may be acting on the axis of rotation.

(c) The forces may be acting parallel to the axis of rotation.

(d) The torque caused by some forces may be equal and opposite to that caused by other forces

Choose the correct alternatives:

(a) For a general rotational motion, angular momentum L and angular velocity ω need not be parallel.

(b) For a rotational motion about a fixed axis, angular momentum L and angular velocity ω are always parallel.

(c) For a general translational motion , momentum p and velocity v are always parallel.

(d) For a general translational motion, acceleration a and velocity v are always parallel.

A Merry-go-round, made of a ring-like platform of radius R and mass M, is revolving with angular speed ω . A person of mass M is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round afterwards is

(a) 2ω

(b) ω

(c) 2 ω

(d) 0