The displacement time graph of a particle moving along a straight line is drawn below.

The accelerations of the particle during the regions  OP, PQ  and  QR

• OP	PQ	QR
  -	0	+

• OP	PQ	QR
  +	0	+

• OP	PQ	QR
  +	0	-

• OP	PQ	QR
  -	+	-

A particle of mass m moves with constant speed along a circular path of radius r under the action of force F. Its speed is

• $\sqrt{\frac{\mathrm{F} \mathrm{r}}{\mathrm{m}}}$

• $\sqrt{\frac{\mathrm{F}}{\mathrm{r}}}$

• $\sqrt{\mathrm{Fmr}}$

• $\sqrt{\frac{\mathrm{F}}{\mathrm{m} \mathrm{r}}}$

A bullet is fired from a rifle and recoils. Kinetic energy of rifile is

• less than K.E of bullet

• greater than K.E of bullet

• equal to K.E of bullet

• none of the above

Side of an equilateral triangle is l. Three point masses each of magnitude m, are placed at the three vertices of the triangle. Moment of inertia of this system about one side of the triangle as axis is given by

• $\frac{3\mathrm{m} {\mathrm{l}}^2}{4}$

• $\frac{4}{3}{\mathrm{ml}}^2$

• $\frac{3}{2}{\mathrm{ml}}^2$

• $\frac{2}{3}{\mathrm{ml}}^2$

P, Q and R are three coplanar forces acting at a point and are in equilibrium. Given: P = 1.9318 kg wt [sin θ₁ = 0.9659], the value of R (in kg wt) is

• 0.9659

• 2

• 1

• 1/2

Suppose  the gravitational  force varies inversely as the  n^th  power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to

• ${\mathrm{R}}^{\left(\frac{\mathrm{n} + 1}{2}\right)}$

• ${\mathrm{R}}^{\left(\frac{\mathrm{n} - 1}{2}\right)}$

• Rⁿ

• ${\mathrm{R}}^{\left(\frac{\mathrm{n} - 2}{2}\right)}$

Figure shows the variation of energy with the orbit radius r of a satellite  in a circular motion. Mark the correct statement

• C is total energy, B kinetic energy and A is potential energy.

• A is kinetic energy, B total energy and C potential energy

• A and 8 are the kinetic and potential energies and C the total energy of the satellite.

• C and A arc kinetic and potential energy respectively and B the total energy of the satellite.

The curve between log_e  $\frac{\mathrm{J}}{{\mathrm{T}}^2}$  and  $\frac{1}{\mathrm{T}}$ is

Assertion: When the velocity of projection of a body is made  n times, its time of flight becomes n  times.

Reason: Range of projectile does not depend on
the initial velocity of a body.

• 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

A slab consists of two layers of different materials of the same thickness and having thermal conductivities  K₁ and K₂  are connected in series. The equivalent thermal conductivity of the slab is

• $\frac{2 {\mathrm{K}}_1 {\mathrm{K}}_2}{{\mathrm{K}}_1 + {\mathrm{K}}_2}$

• $\sqrt{{\mathrm{K}}_1 {\mathrm{K}}_2}$

• $\frac{{\mathrm{K}}_1 {\mathrm{K}}_2}{{\mathrm{K}}_1 + {\mathrm{K}}_2}$

• K₁ + K₂