Understanding of Field

Q.

The length of the second pendulum on the surface of earth is 1 m. The length of seconds pendulum on the surface of moon, where g is 1/6th value of g on the surface of earth, is

1. 1/6 m

2. 6 m

3. 36 m

4. 1/36 m

Q.

The acceleration of a body due to the attraction of the earth (radius R) at a distance 2R from the surface of the earth is (g = acceleration due to gravity at the surface of the earth)

1. 

2. 

3. 

4. 

Q. If W1, W2 and W3 represents the work done in moving a particle from A to B along three different paths 1, 2 and 3, respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W3.

1. W1 > W2 > W3
2. W1 = W2 = W3
3. W1 < W2 < W3
4. W2 > W1 > W3

Q.

A point $\rho$ lies on the axis of a ring of mass M and radius $\alpha$, at a distance $\alpha$, from its centre C, A small particle starts from $\rho$ and reaches C under gravitational attraction only.Its speed at C will be

1. 

2. 

3. 

4. Zero

Q. in a place gravitational field intensity is E=25(i^+j^)N/m.s.what is the work done to bring body of 4kg from point (0, 0) to (2m, 3m)

Q. The density of a newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be

1. $2R$
2. $4R$
3. $\frac{R}{4}$
4. $\frac{R}{2}$

Q.

The acceleration of a body due to the attraction of the earth (radius R) at a distance 2R from the surface of the earth is (g = acceleration due to gravity at the surface of the earth)

1. $\frac{g}{9}$

2. $\frac{g}{3}$

3. $\frac{g}{4}$

4. $g$

Q. The gravitational field in a region is given by $\mathrm{E}=\left(2\overrightarrow{i}+3\overrightarrow{j}\right)\mathrm{N}{\mathrm{kg}}^{-1}$. Show that no work is done by the gravitational field when a particle is moved on the line 3y + 2x = 5.

[Hint : If a line y = mx + c makes angle θ with the X-axis, m = tan θ.]

Q. The density of a newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be

1. $2R$
2. $4R$
3. $\frac{R}{4}$
4. $\frac{R}{2}$

Q. There exists a spherically symmetric gravitational system of particles of radius $R$. Its speed $V$ as a function of distance $r(0<r<\infty )$ from the centre of the system is represented by

1. 
2. 
3. 
4. 

Q. If momentum of a particle is decreased by $x\%$, then K.E is decreased by 36%. Find $x$.

1. 20%
2. 6%
3. 12%
4. 72%