A force F acting on an object varies with distance x as shown in the figure. The force is in N and x in m. The work done by the force in moving the object from x = 0 to  x  = 6 m is

• 13.5 J

• 10 J

• 15 J

• 20 J

A body is moved along a straight line by a machine delivering constant power. The distance travelled by the body in  time t is proportional to

• t^1/2

• t

• t^3/2

• t²

3.

A body is projected horizontally with a velocity 4$\sqrt{2}$  m/sec. The velocity of the body after 0.7 seconds will be nearly ( Take g = 10 m/sec² )

• 10 m/sec

• 9 m/sec

• 19 m/sec

• 11 m/sec

Three equal weights of 3 kg each are hanging on a string passing over a frictionless pulley as shown in figure. The tension in the string between masses  II  and  III  will be ( Take  g = 10 m/sec² )

• 5 N

• 6 N

• 10 N

• 20 N

A  ball  is  bouncing  down  a  flight of stairs. The  coefficient  of  restitution  is  e. The  height of  each  step  is  d  and  the  ball  descends one  step  each  bounce. After  each  bounce  it   rebounds  to  a  height h  above  the  next  lower  step. The  height  is  large  enough  compared  with  the  width of  step  so  that  the  impacts  are  effectively  head-on.  Find the  relationship  between  h  and  d.

• h = $\frac{\mathrm{d}}{1 - {\mathrm{e}}^2}$

• h = $\frac{\mathrm{d}}{1 + {\mathrm{e}}^2}$

• h = $\frac{\mathrm{d}}{1 + \mathrm{e}}$

• h = $\sqrt{\frac{\mathrm{d}}{1 - {\mathrm{e}}^2}}$

A  wire  of  length  l and  mass  m  is  bent  in the  form of  a  semicircle. The   gravitational  field  intensity  at the  centre  of  semicircle  is

• $\frac{\mathrm{G} \mathrm{m}}{\mathrm{\pi } \mathrm{l}}$ along x - axis

• $\frac{\mathrm{G} \mathrm{m}}{\mathrm{\pi } \mathrm{l}}$ along y-axis

• $\frac{2\mathrm{\pi } \mathrm{G} \mathrm{m}}{{\mathrm{l}}^2}$ along y-axis

• $\frac{2 \mathrm{\pi } \mathrm{G} \mathrm{m}}{{\mathrm{l}}^2}$ along x-axis

Assertion:  Generally  the  path  of  a  projectile from  the  earth  is  parabolic  but  it  is elliptical  for  projectiles  going  to  a very  great  height.

Reason:  Up to ordinary height the  projectile  moves under  a  uniform  gravitational  force, but  for  great  heights,  projectile  moves  under a  variable force.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false.

Assertion:  Angular  speed  of  a  planet  around  the  sun  increases,  when  it  is  closer to the sun.

Reason: Total angular momentum of the system remains constant.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

Assertion:  Impulsive  force  is  large  and  acts  for a short time.

Reason: Finite  change  in  momentum  should  be  produced  by  the  force.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

Which of the following graph depicts spring constant k versus length l of the spring correctly?