A thin uniform rod of length

Let P(r) = Qr/πR⁴ be the charge density distribution for a solid sphere of radius R and total charge Q. for a point ‘p’ inside the sphere at distance r₁ from the centre of the sphere, the magnitude of electric field is

• 

• 0

• 
• 

A particle has an initial velocity of  and an acceleration of It speed after 10 s

• 10 units

• 

• 7 units

• 7 units

A motorcycle starts from rest and accelerates along a straight path at 2 m/s². At the straight point of the motorcycle, there is a stationary electric siren. How far has the motorcycle gone when the driver hears the frequency of the siren at 94% of its value when the motorcycle was at rest?

• 49 m

• 98 m

• 147 m

• 147 m

Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate.Assume that the duration of collision is negligible and the collision with the plate is totally elastic.Then the velocity as a function of time and the height as a function of time will be

In an experiment, the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half–a–degree (= 0.5o° ), then the least count of the instrument is

• one minute

• half minute

• One degree

• One degree

The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is

• 2R

• 

• R/2

• R/2

If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

• a²T²+ 4π²v²

• aT/x

• aT + 2πv

• aT + 2πv

One kg of a diatomic gas is at a pressure of 8 × 10⁴ N/m² . The density of the gas is 4 kg/m^-3. What is the energy of the gas due to its thermal motion?

• 3 × 10⁴ J

• 5× 10⁴ J

• 6× 10⁴ J

• 6× 10⁴ J

Two points P and Q are maintained at the potential of 10V and -4V respectively. The work done in moving 100 electrons from P to Q is 

• 9.60 × 10^–17 J 

• 9.60 × 10^–17 J

• – 2.24 × 10^–16 J 

• – 2.24 × 10^–16 J