A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of

• 81

• 1/81

• 9

• 1/9

C.

9

A pendulum made of a uniform wire of cross-sectional area A has time period T. When an additional mass M is added to its Bob, the time period changes TM. If Young's modulus of the material of the wire is Y, then 1/Y is equal to (g = gravitational acceleration)

• 
• 
• 
• 

A.

Time period,
When additional mass M is added to its Bob
 where Δ is increase in length
As we know that,

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1 %. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 10³ kg/m³ and 2.2 × 10¹¹N/m² respectively?

• 188.5 Hz

• 178.2 Hz

• 200.5 Hz

• 770 Hz

B.

178.2 Hz

A transparent solid cylindrical rod has a refractive index of 2√3. It is surrounded by air. A light ray is incident at the midpoint of one end of the rod as shown in the figure.θ The incident angle θ for which the light ray grazes along the wall of the rod is 

• 
• 
• 
• 

D.

A wooden wheel of radius R is made of two semicircular parts (see figure); The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that it temperature rises by ∆T and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is α, and its Youngs'modulus is Y, the force that one part of the wheel applies on the other part is :

• 2πSYα∆T

• SYα∆T

• πSYα ∆T

• 2SYα ∆T