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21.

The pressure  that has to be applied in the ends of a steel wire of length  10cm to keep its length  constant  when  its temperature is raised by 100° C  is (For  steel, Young's modulus  is   $2\times 10^{11}Nm^{-2}$ and coefficient of thermal expansion is $1.1\times 10^{-5}K^{-1}$ )

A) $2.2\times 10^{8}Pa$

B) $2.2\times 10^{9}Pa$

C) $2.2\times 10^{7}Pa$

D) $2.2\times 10^{6}Pa$

22.

Four particles, each  of mass M and equidistant from each other,  move along  a circle of radius  R under the action  of their mutual  gravitational attraction, the speed of each particle

A) $\sqrt{\frac{GM^{}}{R^{}}}$

B) $\sqrt{2\sqrt{2}\frac{GM^{}}{R^{}}}$

C) $\sqrt{\frac{GM^{}}{R^{}}(1+2\sqrt{2})}$

D) $\frac{1}{2}\sqrt{\frac{GM^{}}{R^{}}(2\sqrt{2}+1)}$

23.

A bob of mass m attached to an inextensible string of length l is suspended from a vertical support . The bob rotates  in a horizontal circle with an angular speed ω  rad/s about the vertical support, About  the point of suspension

A) angular momentum is conserved

B) angular momentum changes magnitude but not in direction

C) angular momentum changes direction but not in magnitude

D) angular momentum changes both in direction and magnitude

24.

When a rubber band is stretched by a distance x, it exerts a restoring force of magnitude  $F=ax+bx^{2}$ , where a and b are constants. The work done in stretching the unstretched runner-band  by L is

A) $aL^{2}+bL^{3}$

B) $\frac{1}{2}(aL^{2}+bL^{3})$

C) $\frac{aL^{2}}{2}+\frac{bL^{3}}{3}$

D) $\frac{1}{2}\left(\frac{aL^{2}}{2}+\frac{bL^{3}}{3}\right)$

25.

A  block of mass m is placed on a surface with a vertical cross-section given by y=x3/6. If the coefficient of friction is 0.5, the maximum  height above  the ground at which the block can be placed without slipping is

A) $\frac{1}{6}m$

B) $\frac{2}{3}m$

C) $\frac{1}{3}m$

D) $\frac{1}{2}m$

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