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

The kinetic energy K of a rotating body depends on its moment of inertia I and its angular speedω. Assuming the relation to be \[k = KI^0w^B\]  where k is a dimensionless constant, find a and b. Moment of inertia of a sphere about its diameter is  \[\frac{2}{5}M r^2\] 

The velocity of a particle is towards west at an instant. Its acceleration is not towards west, not towards east, not towards north and towards south. Give an example of this type of motion .

A particle moves on a given straight line with a constant speed ν. At a certain time it is at a point P on its straight line path. O is a fixed point. Show that \[\vec{OP} \times \vec{\nu}\] is independent of the position P.

The force on a charged particle due to electric and magnetic fields is given by \[\vec{F} = q \vec{E} + q \vec{\nu} \times \vec{B}\].
Suppose \[\vec{E}\]  is along the X-axis and \[\vec{B}\]  along the Y-axis. In what direction and with what minimum speed ν should a positively charged particle be sent so that the net force on it is zero?

In a projectile motion the velocity 

Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit he ground first? 

The electric current in a discharging R−C circuit is given by i = i₀ e^−t/RC where i₀, R and C are constant parameters and t is time. Let i₀ = 2⋅00 A, R = 6⋅00 × 10⁵ Ω and C = 0⋅500 μF. (a) Find the current at t = 0⋅3 s. (b) Find the rate of change of current at at 0⋅3 s. (c) Find approximately the current at t = 0⋅31 s.

Find the area bounded under the curve y = 3x² + 6x + 7 and the X-axis with the ordinates at x = 5 and x = 10.

Find the area enclosed by the curve y = sin x and the X-axis between x = 0 and x = π.

Find the area bounded by the curve y = e^−x, the X-axis and the Y-axis.

A rod of length L is placed along the X-axis between x = 0 and x = L. The linear density (mass/length) ρ of the rod varies with the distance x from the origin as ρ = a + bx. (a) Find the SI units of a and b. (b) Find the mass of the rod in terms of a, b and L.

A metre scale is graduated at every millimetre. How many significant digits will be there in a length measurement with this scale?

A train starts from rest and moves with a constant acceleration of 2.0 m/s² for half a minute. The brakes are then applied and the train comes to rest in one minute. Find the total distance moved by the train.

A train starts from rest and moves with a constant acceleration of 2.0 m/s² for half a minute. The brakes are then applied and the train comes to rest in one minute. Find  the maximum speed attained by the train .

A train starts from rest and moves with a constant acceleration of 2.0 m/s² for half a minute. The brakes are then applied and the train comes to rest in one minute. Find the position(s) of the train at half the maximum speed.

A particle starting from rest moves with constant acceleration. If it takes 5.0 s to reach the speed 18.0 km/h find the average velocity during this period .