A body is displaced from (0,0) to (1m,1m) along the path x=y by a force $F=\left(x^2\hat{j}+y\hat{i}\right)N$. The work done by this force will be :

1. $\frac{4}{3}J$

2. $\frac{5}{6}J$

3. $\frac{3}{2}J$

4. $\frac{7}{5}J$

A stone is projected from a horizontal plane. It attains maximum height, \(H\), and strikes a stationary smooth wall & falls on the ground vertically below the maximum height. Assuming the collision to be elastic, the height of the point on the wall where the ball will strike will be:

A weightless rod of length 2l carries two equal mass 'm', one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in a vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in the horizontal position. The speed of the mass B at the instant rod becomes vertical is:

1. \(\sqrt{\frac{3 g l}{5}} \)

2. \(\sqrt{\frac{4 g l}{5}} \)

3. \(\sqrt{\frac{6 g l}{5}} \)

4. \(\sqrt{\frac{7 g l}{5}} \)

A body of mass (m) elastically collides with another stationary body of mass 3m. The fractional loss of K.E. of the body is:

1.  $\frac{8}{9}$

2.  $\frac{3}{4}$

3.  $\frac{3}{5}$

4.  $\frac{4}{7}$

A force F is applied on a body which moves with a velocity v in the direction of the force, then the power will be

1.  ${\mathrm{Fv}}^2$

2.  Fv

3.  $\mathrm{F}/{\mathrm{v}}^2$

4.  F/v

Potential energy \((U)\) related to coordinates is given by; \(U=3(x+y).\) Work done by the conservative force when the particle is going from \((0,0), (2,3)\) is:
1. \(15\) J
2. \(-15\) J
3. \(12\) J
4. \(10\) J

A mass m slips along the wall of a semispherical surface of radius R. The velocity at the bottom of the surface is [ MP PMT 1993]

(1) $\sqrt{Rg}$

(2) $\sqrt{2Rg}$

(3) $2\sqrt{\pi Rg}$

(4) $\sqrt{\pi Rg}$

Three different objects of mass $m_1,$ $m_2$ and m₃ are allowed to fall from rest and from the same point ‘O’ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of:

When a body moves with a constant speed along a circle 

(1) No work is done on it

(2) No acceleration is produced in the body

(3) No force acts on the body

(4) Its velocity remains constant

A sphere of mass m is tied to end of a string of length l and rotated through the other end along a horizontal circular path with speed v. The work done by centripetal force in full horizontal circle is 

(1) 0

(2) $\left(\frac{{\displaystyle m{v}^2}}{{\displaystyle l}}\right)\hspace{0.17em}.\hspace{0.17em}2\pi l$

(3) $\text{mg\hspace{0.17em}.\hspace{0.17em}2πl}$

(4) $\left(\frac{{\displaystyle m{v}^2}}{{\displaystyle l}}\right)\hspace{0.17em}.\hspace{0.17em}\left(l\right)$