126. A spur gear wi t h 20° full dept h teeth i s transmitting 20 kW at 200 rad/s. The pitch circle diameter of the gear is 100 mm. The magnitude of the force applied on the gear in the radial direction is
     

1. 1. 0.36 kN
      

   
   
   

   2. 2.78 kN
      

   
   
   

   3. 0.73 kN
      

   
   
   

   4. 1.39 kN

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given: φ = 20°
   P = 20 kW, ω = 200 rad/s Pitch Circle Diameter = 100 mm
   Now, force on radial direction (F_r),
   
   

   Now ,	Fr	=	F sinφ	= tanφ
   	Ft		F cosφ

   
   ⇒ F_r = F_t tanφ
   

   Also , T =	P	=	20 × 1000	= 100 N-m
   	ω		200

   
   T = F_t × r
   

   Ft =	T	=	100	= 2000 N
   	r		(100/2) × 10-3

   
   F_r = F_t tan φ = 2000 tan 20 = 727.9 N
   = 727.9 × 10^-3 kN = 0.73 kN

   Correct Option: C

   Given: φ = 20°
   P = 20 kW, ω = 200 rad/s Pitch Circle Diameter = 100 mm
   Now, force on radial direction (F_r),
   
   

   Now ,	Fr	=	F sinφ	= tanφ
   	Ft		F cosφ

   
   ⇒ F_r = F_t tanφ
   

   Also , T =	P	=	20 × 1000	= 100 N-m
   	ω		200

   
   T = F_t × r
   

   Ft =	T	=	100	= 2000 N
   	r		(100/2) × 10-3

   
   F_r = F_t tan φ = 2000 tan 20 = 727.9 N
   = 727.9 × 10^-3 kN = 0.73 kN

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127. It is desired to avoid interference in a pair of spur gears having a 20° pressure angle. With increase in pinion to gear speed ratio, the minimum number of teeth on the pinion
     

1. 1. increases
      

   
   
   

   2. decreases
      

   
   
   

   3. first increases and then decreases
      

   
   
   

   4. remains unchanged

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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128. The following are the data for two crossed helical gears used for speed reduction:
     Gear I: Pitch circle diameter in the plane of rotation 80 mm and helix angle 30°
     Gear II: Pitch circle diameter in the plane of rotation 120 mm and helix angle 22.5°
     If the input speed is 1440 rpm, the output speed in rpm is
     

1. 1. 1200
      

   
   
   

   2. 900
      

   
   
   

   3. 875
      

   
   
   

   4. 720

   
   
   

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1. View Hint View Answer Discuss in Forum

   For helical gears
   

   Velocity ratio =	d1 cosφ
   	d1 cosφ

   
   

   =	80 cos30°	=	N2
   	120 cos22.5°		N1

   
   ∴ N₂ = 1440 × 0.625 = 900 rpm

   Correct Option: B

   For helical gears
   

   Velocity ratio =	d1 cosφ
   	d1 cosφ

   
   

   =	80 cos30°	=	N2
   	120 cos22.5°		N1

   
   ∴ N₂ = 1440 × 0.625 = 900 rpm

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129. Tooth interference in an external involute spur gear pair can be reduced by

1. 1. decreasing center distance between gear pair
      

   
   
   

   2. decreasing module
      

   
   
   

   3. decreasing pressure angle
      

   
   
   

   4. increasing number of gear teeth

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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130. A concentrated mass m is attached at the centre of a rod of Iength 2L as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is
     
     
     

1. 1. √k / m
      

   
   
   

   2. √2k / m
      

   
   
   

   3. √k / 2m
      

   
   
   

   4. √4k / m
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Equation of motion, is
   m( Lθ̇ ).Lθ + kx × 2 L = 0
   ⇒ m( Lθ̇ ).Lθ + k(2L.θ) × 2 L = 0
   ⇒ mL²θ̇̇ + 4kL² θ = 0
   ⇒ θ̇̇ + √4k / mθ = 0
   

   ∴ ωn = √	4k
   	m

   Correct Option: D

   
   Equation of motion, is
   m( Lθ̇ ).Lθ + kx × 2 L = 0
   ⇒ m( Lθ̇ ).Lθ + k(2L.θ) × 2 L = 0
   ⇒ mL²θ̇̇ + 4kL² θ = 0
   ⇒ θ̇̇ + √4k / mθ = 0
   

   ∴ ωn = √	4k
   	m

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